Equivalent Expressions - ACT Math
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What is the power of a product rule?
What is the power of a product rule?
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$(ab)^n=a^n b^n$. Distribute the exponent to each factor in the product.
$(ab)^n=a^n b^n$. Distribute the exponent to each factor in the product.
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What is the equivalent expression for $5x-3(x+2)$ after simplifying?
What is the equivalent expression for $5x-3(x+2)$ after simplifying?
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$2x-6$. Distribute first, then combine like terms.
$2x-6$. Distribute first, then combine like terms.
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What is the simplified form of $7x + 3 - 4x$?
What is the simplified form of $7x + 3 - 4x$?
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$3x + 3$. Combine like terms: $7x - 4x = 3x$.
$3x + 3$. Combine like terms: $7x - 4x = 3x$.
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Which expression is equivalent to $a^2 - 2a + 1$?
Which expression is equivalent to $a^2 - 2a + 1$?
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$(a - 1)^2$. Perfect square trinomial with pattern $a^2 - 2ab + b^2 = (a - b)^2$.
$(a - 1)^2$. Perfect square trinomial with pattern $a^2 - 2ab + b^2 = (a - b)^2$.
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What is the equivalent expression for $x^2 - 9$?
What is the equivalent expression for $x^2 - 9$?
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$(x - 3)(x + 3)$. Difference of squares pattern: $a^2 - b^2 = (a - b)(a + b)$.
$(x - 3)(x + 3)$. Difference of squares pattern: $a^2 - b^2 = (a - b)(a + b)$.
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What is the definition of equivalence for expressions?
What is the definition of equivalence for expressions?
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Same value for all allowed variable values. Two expressions that always produce identical results.
Same value for all allowed variable values. Two expressions that always produce identical results.
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What is an equivalent expression for $4a^2 - 9b^2$?
What is an equivalent expression for $4a^2 - 9b^2$?
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$(2a - 3b)(2a + 3b)$. Difference of squares pattern with $a = 2a$ and $b = 3b$.
$(2a - 3b)(2a + 3b)$. Difference of squares pattern with $a = 2a$ and $b = 3b$.
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Factor the expression $x^2 + 5x + 6$.
Factor the expression $x^2 + 5x + 6$.
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$(x + 2)(x + 3)$. Find two numbers that multiply to 6 and add to 5.
$(x + 2)(x + 3)$. Find two numbers that multiply to 6 and add to 5.
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Rewrite $15x - 10$ as a product of factors.
Rewrite $15x - 10$ as a product of factors.
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$5(3x - 2)$. Factor out the greatest common factor 5.
$5(3x - 2)$. Factor out the greatest common factor 5.
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Find the equivalent expression for $3(a + b) - 2a$.
Find the equivalent expression for $3(a + b) - 2a$.
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$a + 3b$. Distribute 3, then combine like terms: $3a + 3b - 2a$.
$a + 3b$. Distribute 3, then combine like terms: $3a + 3b - 2a$.
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What is the simplified form of $\frac{6x^2}{3x}$?
What is the simplified form of $\frac{6x^2}{3x}$?
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$2x$. Divide coefficients and subtract exponents: $\frac{6}{3} \cdot \frac{x^2}{x}$.
$2x$. Divide coefficients and subtract exponents: $\frac{6}{3} \cdot \frac{x^2}{x}$.
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What is the factored form of $x^2 - 4$?
What is the factored form of $x^2 - 4$?
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$(x + 2)(x - 2)$. Difference of squares: $x^2 - 4 = x^2 - 2^2$.
$(x + 2)(x - 2)$. Difference of squares: $x^2 - 4 = x^2 - 2^2$.
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Find the equivalent expression for $x^2 - 8x + 16$.
Find the equivalent expression for $x^2 - 8x + 16$.
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$(x - 4)^2$. Perfect square trinomial: $(x-4)^2 = x^2 - 8x + 16$.
$(x - 4)^2$. Perfect square trinomial: $(x-4)^2 = x^2 - 8x + 16$.
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Find the equivalent expression for $x^2 - 10x + 25$.
Find the equivalent expression for $x^2 - 10x + 25$.
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$(x - 5)^2$. Perfect square trinomial: $(x-5)^2 = x^2 - 10x + 25$.
$(x - 5)^2$. Perfect square trinomial: $(x-5)^2 = x^2 - 10x + 25$.
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What is the equivalent expression for $a^2 - 2ab + b^2$?
What is the equivalent expression for $a^2 - 2ab + b^2$?
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$(a - b)^2$. Perfect square trinomial pattern with $a$ and $b$.
$(a - b)^2$. Perfect square trinomial pattern with $a$ and $b$.
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Which expression is equivalent to $9 - x^2$?
Which expression is equivalent to $9 - x^2$?
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$(3 - x)(3 + x)$. Difference of squares: $9 - x^2 = 3^2 - x^2$.
$(3 - x)(3 + x)$. Difference of squares: $9 - x^2 = 3^2 - x^2$.
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What is the simplified form of $5x - (2x - 4)$?
What is the simplified form of $5x - (2x - 4)$?
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$3x + 4$. Distribute negative sign, then combine: $5x - 2x + 4$.
$3x + 4$. Distribute negative sign, then combine: $5x - 2x + 4$.
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Which expression is equivalent to $x^2 + 4x + 4$?
Which expression is equivalent to $x^2 + 4x + 4$?
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$(x + 2)^2$. Perfect square trinomial with $a=x$ and $b=2$.
$(x + 2)^2$. Perfect square trinomial with $a=x$ and $b=2$.
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Which expression is equivalent to $x^2 - 2x + 1$?
Which expression is equivalent to $x^2 - 2x + 1$?
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$(x - 1)^2$. Perfect square trinomial with $a=x$ and $b=1$.
$(x - 1)^2$. Perfect square trinomial with $a=x$ and $b=1$.
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What is the factored form of $x^2 - 5x + 6$?
What is the factored form of $x^2 - 5x + 6$?
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$(x - 2)(x - 3)$. Find two numbers that multiply to 6 and add to $-5$.
$(x - 2)(x - 3)$. Find two numbers that multiply to 6 and add to $-5$.
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What is the factored form of $x^2 + 7x + 10$?
What is the factored form of $x^2 + 7x + 10$?
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$(x + 2)(x + 5)$. Find two numbers that multiply to 10 and add to 7.
$(x + 2)(x + 5)$. Find two numbers that multiply to 10 and add to 7.
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Identify the equivalent expression for $4(x + 2) + 3x$.
Identify the equivalent expression for $4(x + 2) + 3x$.
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$7x + 8$. Distribute 4, then combine like terms: $4x + 8 + 3x$.
$7x + 8$. Distribute 4, then combine like terms: $4x + 8 + 3x$.
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Find the equivalent expression for $x^2 + 2xy + y^2$.
Find the equivalent expression for $x^2 + 2xy + y^2$.
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$(x + y)^2$. Perfect square trinomial with variables $x$ and $y$.
$(x + y)^2$. Perfect square trinomial with variables $x$ and $y$.
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What is the factored form of $x^2 + 5x + 6$?
What is the factored form of $x^2 + 5x + 6$?
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$(x + 2)(x + 3)$. Find two numbers that multiply to 6 and add to 5.
$(x + 2)(x + 3)$. Find two numbers that multiply to 6 and add to 5.
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Identify the equivalent expression for $6x - 2(x + 3)$.
Identify the equivalent expression for $6x - 2(x + 3)$.
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$4x - 6$. Distribute $-2$, then combine: $6x - 2x - 6$.
$4x - 6$. Distribute $-2$, then combine: $6x - 2x - 6$.
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Find the equivalent expression for $x^2 - 6x + 9$.
Find the equivalent expression for $x^2 - 6x + 9$.
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$(x - 3)^2$. Perfect square trinomial: $(a-b)^2 = a^2 - 2ab + b^2$.
$(x - 3)^2$. Perfect square trinomial: $(a-b)^2 = a^2 - 2ab + b^2$.
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Which expression is equivalent to $3(x - 4) + 2x$?
Which expression is equivalent to $3(x - 4) + 2x$?
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$5x - 12$. Distribute 3, then combine like terms: $3x - 12 + 2x$.
$5x - 12$. Distribute 3, then combine like terms: $3x - 12 + 2x$.
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What is the simplified form of $8x - 3x + 5$?
What is the simplified form of $8x - 3x + 5$?
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$5x + 5$. Combine like terms: $8x - 3x = 5x$.
$5x + 5$. Combine like terms: $8x - 3x = 5x$.
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What is the simplified form of $4x - 2(3x - 5)$?
What is the simplified form of $4x - 2(3x - 5)$?
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$-2x + 10$. Distribute $-2$, then combine like terms: $4x - 6x + 10$.
$-2x + 10$. Distribute $-2$, then combine like terms: $4x - 6x + 10$.
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Identify the equivalent expression for $2(x + 3) + 4x$.
Identify the equivalent expression for $2(x + 3) + 4x$.
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$6x + 6$. Distribute 2, then combine like terms: $2x + 6 + 4x$.
$6x + 6$. Distribute 2, then combine like terms: $2x + 6 + 4x$.
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