Equivalent Expressions - PSAT Math
Card 1 of 30
What is an equivalent expression to $(x+5)^2$?
What is an equivalent expression to $(x+5)^2$?
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$x^2+10x+25$. Use $(a+b)^2=a^2+2ab+b^2$ with $a=x$ and $b=5$.
$x^2+10x+25$. Use $(a+b)^2=a^2+2ab+b^2$ with $a=x$ and $b=5$.
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What is the correct expansion of $3(x-4)$?
What is the correct expansion of $3(x-4)$?
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$3x-12$. Distribute: $3 \cdot x = 3x$ and $3 \cdot (-4) = -12$.
$3x-12$. Distribute: $3 \cdot x = 3x$ and $3 \cdot (-4) = -12$.
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What is the distributive property for subtraction, using variables $a$, $b$, and $c$?
What is the distributive property for subtraction, using variables $a$, $b$, and $c$?
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$a(b-c)=ab-ac$. Distribute the factor and keep the subtraction sign.
$a(b-c)=ab-ac$. Distribute the factor and keep the subtraction sign.
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What is the simplified equivalent expression for $\frac{3x}{6}$ in lowest terms?
What is the simplified equivalent expression for $\frac{3x}{6}$ in lowest terms?
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$\frac{x}{2}$. Simplify by dividing both numerator and denominator by $3$.
$\frac{x}{2}$. Simplify by dividing both numerator and denominator by $3$.
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What is the equivalent expression for $2x+3x^2-x+5$ in standard form?
What is the equivalent expression for $2x+3x^2-x+5$ in standard form?
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$3x^2+x+5$. Combine like terms and arrange by degree.
$3x^2+x+5$. Combine like terms and arrange by degree.
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What is the exponent rule for multiplying same-base powers: $a^m\cdot a^n$?
What is the exponent rule for multiplying same-base powers: $a^m\cdot a^n$?
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$a^{m+n}$. When multiplying powers with same base, add the exponents.
$a^{m+n}$. When multiplying powers with same base, add the exponents.
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What is the simplified equivalent expression for $7a-2a+4$?
What is the simplified equivalent expression for $7a-2a+4$?
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$5a+4$. Combine like terms: $7a - 2a = 5a$.
$5a+4$. Combine like terms: $7a - 2a = 5a$.
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What is the simplified equivalent expression for $2x+3x-5$?
What is the simplified equivalent expression for $2x+3x-5$?
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$5x-5$. Combine like terms: $2x + 3x = 5x$.
$5x-5$. Combine like terms: $2x + 3x = 5x$.
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What is the equivalent expression for $6x-9$ after factoring out the GCF $3$?
What is the equivalent expression for $6x-9$ after factoring out the GCF $3$?
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$3(2x-3)$. Factor out the common factor $3$ from both terms.
$3(2x-3)$. Factor out the common factor $3$ from both terms.
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What is the exponent rule for dividing same-base powers: $\frac{a^m}{a^n}$ for $a\ne 0$?
What is the exponent rule for dividing same-base powers: $\frac{a^m}{a^n}$ for $a\ne 0$?
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$a^{m-n}$. When dividing powers with same base, subtract the exponents.
$a^{m-n}$. When dividing powers with same base, subtract the exponents.
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What is the definition of a negative exponent $a^{-n}$ for $a\ne 0$?
What is the definition of a negative exponent $a^{-n}$ for $a\ne 0$?
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$a^{-n}=\frac{1}{a^n}$. A negative exponent means reciprocal with positive exponent.
$a^{-n}=\frac{1}{a^n}$. A negative exponent means reciprocal with positive exponent.
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What is the definition of the zero exponent $a^0$ for $a\ne 0$?
What is the definition of the zero exponent $a^0$ for $a\ne 0$?
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$a^0=1$. Any nonzero number raised to the zero power equals one.
$a^0=1$. Any nonzero number raised to the zero power equals one.
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What is the identity for factoring out $-1$ from an expression $-(a-b)$?
What is the identity for factoring out $-1$ from an expression $-(a-b)$?
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$-(a-b)=-a+b$. Distributing $-1$ changes the sign of each term.
$-(a-b)=-a+b$. Distributing $-1$ changes the sign of each term.
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What is the equivalent expression for $3(x+4)$ after distributing?
What is the equivalent expression for $3(x+4)$ after distributing?
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$3x+12$. Multiply $3$ by each term: $3 \cdot x + 3 \cdot 4$.
$3x+12$. Multiply $3$ by each term: $3 \cdot x + 3 \cdot 4$.
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What is the simplified equivalent expression for $\left(2x^2y\right)^2$?
What is the simplified equivalent expression for $\left(2x^2y\right)^2$?
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$4x^4y^2$. Apply power rule: $2^2 \cdot (x^2)^2 \cdot y^2 = 4x^4y^2$.
$4x^4y^2$. Apply power rule: $2^2 \cdot (x^2)^2 \cdot y^2 = 4x^4y^2$.
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What is the equivalent expression for $4x+12$ after factoring out the GCF $4$?
What is the equivalent expression for $4x+12$ after factoring out the GCF $4$?
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$4(x+3)$. Factor out the common factor $4$ from both terms.
$4(x+3)$. Factor out the common factor $4$ from both terms.
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What is the equivalent expression for $5(2x-3)$ after distributing?
What is the equivalent expression for $5(2x-3)$ after distributing?
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$10x-15$. Multiply $5$ by each term: $5 \cdot 2x + 5 \cdot (-3)$.
$10x-15$. Multiply $5$ by each term: $5 \cdot 2x + 5 \cdot (-3)$.
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What is the simplified equivalent expression for $\frac{x^5}{x^2}$ for $x\ne 0$?
What is the simplified equivalent expression for $\frac{x^5}{x^2}$ for $x\ne 0$?
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$x^3$. Apply quotient rule: $x^{5-2} = x^3$.
$x^3$. Apply quotient rule: $x^{5-2} = x^3$.
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What is the equivalent expression for $-2(x-7)$ after distributing?
What is the equivalent expression for $-2(x-7)$ after distributing?
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$-2x+14$. Distribute $-2$: $-2 \cdot x + (-2) \cdot (-7) = -2x + 14$.
$-2x+14$. Distribute $-2$: $-2 \cdot x + (-2) \cdot (-7) = -2x + 14$.
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What is an equivalent expression to $(2x^3)^2$?
What is an equivalent expression to $(2x^3)^2$?
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$4x^6$. Apply power rule: $(2)^2=4$ and $(x^3)^2=x^6$.
$4x^6$. Apply power rule: $(2)^2=4$ and $(x^3)^2=x^6$.
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Which expression is equivalent to $\frac{1}{2}(8x+6)$?
Which expression is equivalent to $\frac{1}{2}(8x+6)$?
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$4x+3$. Distribute $\frac{1}{2}$: $\frac{1}{2}\cdot^8x=4x$ and $\frac{1}{2}\cdot^6=3$.
$4x+3$. Distribute $\frac{1}{2}$: $\frac{1}{2}\cdot^8x=4x$ and $\frac{1}{2}\cdot^6=3$.
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What is an equivalent expression to $4a^2\cdot 3a^5$?
What is an equivalent expression to $4a^2\cdot 3a^5$?
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$12a^7$. Multiply coefficients and add exponents: $4\cdot^3=12$, $a^{2+5}=a^7$.
$12a^7$. Multiply coefficients and add exponents: $4\cdot^3=12$, $a^{2+5}=a^7$.
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What is an equivalent expression to $\frac{6x^4}{2x}$?
What is an equivalent expression to $\frac{6x^4}{2x}$?
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$3x^3$. Divide coefficients and subtract exponents: $\frac{6}{2}=3$, $x^{4-1}=x^3$.
$3x^3$. Divide coefficients and subtract exponents: $\frac{6}{2}=3$, $x^{4-1}=x^3$.
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What is an equivalent factored form of $x^2-16$?
What is an equivalent factored form of $x^2-16$?
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$(x-4)(x+4)$. Recognize $16=4^2$, so $x^2-16=x^2-4^2$ is a difference of squares.
$(x-4)(x+4)$. Recognize $16=4^2$, so $x^2-16=x^2-4^2$ is a difference of squares.
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What is an equivalent expression to $7(x-2)+3(x-2)$?
What is an equivalent expression to $7(x-2)+3(x-2)$?
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$10(x-2)$. Factor out common term $(x-2)$: $7+3=10$.
$10(x-2)$. Factor out common term $(x-2)$: $7+3=10$.
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What is an equivalent expression to $2x+7x-4$?
What is an equivalent expression to $2x+7x-4$?
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$9x-4$. Combine like terms: $2x+7x=9x$.
$9x-4$. Combine like terms: $2x+7x=9x$.
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What is an equivalent expression to $5x-2(x-3)$?
What is an equivalent expression to $5x-2(x-3)$?
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$3x+6$. Distribute $-2$, then combine like terms: $5x-2x+6=3x+6$.
$3x+6$. Distribute $-2$, then combine like terms: $5x-2x+6=3x+6$.
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What is an equivalent expression to $3(x+4)$?
What is an equivalent expression to $3(x+4)$?
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$3x+12$. Distribute $3$ to both $x$ and $4$.
$3x+12$. Distribute $3$ to both $x$ and $4$.
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What is the definition of like terms?
What is the definition of like terms?
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Terms with the same variable part and exponents. Like terms can be combined because they have identical variables.
Terms with the same variable part and exponents. Like terms can be combined because they have identical variables.
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What is the definition of a term in an algebraic expression?
What is the definition of a term in an algebraic expression?
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A part separated by addition or subtraction. Terms are the individual parts combined by $+$ or $-$.
A part separated by addition or subtraction. Terms are the individual parts combined by $+$ or $-$.
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