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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #6 : Monomials

Simplify the following

$(7y)(7t-3y^{3} + 2)$ $\displaystyle (7y)(7t-3y^{3} + 2)$

Possible Answers:

$49yt-21y^{4} +14y$ $\displaystyle 49yt-21y^{4} +14y$

$49yt-21y^{2} +14y$ $\displaystyle 49yt-21y^{2} +14y$

$14yt-10y^{4} +14y$ $\displaystyle 14yt-10y^{4} +14y$

$14yt-21y^{4} +14y$ $\displaystyle 14yt-21y^{4} +14y$

$28y-21y^{4} +14t$ $\displaystyle 28y-21y^{4} +14t$

Correct answer:

$49yt-21y^{4} +14y$ $\displaystyle 49yt-21y^{4} +14y$

Explanation:

Distribute $\displaystyle 7y$ to each term in the parentheses in the polynomial

$\displaystyle 7y(7t)=49yt$

$7y(-3y^{3})=-21y^{4}$ $\displaystyle 7y(-3y^{3})=-21y^{4}$

$\displaystyle 7y(2)=14y$

Combine the results

$(7y)(7t-3y^{3} + 2)=49yt-21y^{4} +14y$ $\displaystyle (7y)(7t-3y^{3} + 2)=49yt-21y^{4} +14y$

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Example Question #2 : How To Multiply A Monomial By A Polynomial

Expand the expression by multiplying the terms.

$\small (x-4)(x+2)(2x-5)$ $\displaystyle \small (x-4)(x+2)(2x-5)$

Possible Answers:

$\small 2x^3-x^2-26x+40$ $\displaystyle \small 2x^3-x^2-26x+40$

$\small 2x^3+x^2-26x+40$ $\displaystyle \small 2x^3+x^2-26x+40$

$\small 2x^3+9x^2-6x+40$ $\displaystyle \small 2x^3+9x^2-6x+40$

$\small 2x^3-9x^2-6x+40$ $\displaystyle \small 2x^3-9x^2-6x+40$

Correct answer:

$\small 2x^3-9x^2-6x+40$ $\displaystyle \small 2x^3-9x^2-6x+40$

Explanation:

$\small (x-4)(x+2)(2x-5)$ $\displaystyle \small (x-4)(x+2)(2x-5)$

When multiplying, the order in which you multiply does not matter. Let's start with the first two monomials.

$\displaystyle (x-4)(x+2)$

Use FOIL to expand.

$\displaystyle x^2+2x-4x-8=x^2-2x-8$

Now we need to multiply the third monomial.

$\small (x-4)(x+2)(2x-5)=(x^2-2x-8)(2x-5)$ $\displaystyle \small (x-4)(x+2)(2x-5)=(x^2-2x-8)(2x-5)$

Similar to FOIL, we need to multiply each combination of terms.

$\displaystyle 2x(x^2-2x-8)+(-5)(x^2-2x-8)$

$\displaystyle 2x^3-4x^2-16x-5x^2+10x+40$

Combine like terms.

$\displaystyle 2x^3-9x^2-6x+40$

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Example Question #1 : Simplifying Expressions

Find the product:

$\small 7n(8n-2)$ $\displaystyle \small 7n(8n-2)$

Possible Answers:

$\small n^2+14$ $\displaystyle \small n^2+14$

$\small 56n^2-14n$ $\displaystyle \small 56n^2-14n$

$\small n^2-14n$ $\displaystyle \small n^2-14n$

$\small n-14$ $\displaystyle \small n-14$

Correct answer:

$\small 56n^2-14n$ $\displaystyle \small 56n^2-14n$

Explanation:

First, mulitply the mononomial by the first term of the polynomial:

$\small 7n\times8n\ = 56n^2$ $\displaystyle \small 7n\times8n\ = 56n^2$

Second, multiply the monomial by the second term of the polynomial:

$\small 7n\times (-2)\ = -14n$ $\displaystyle \small 7n\times (-2)\ = -14n$

Add the terms together:

$\small 56n^2\ +\ (-14n)\ = 56n^2-14n$ $\displaystyle \small 56n^2\ +\ (-14n)\ = 56n^2-14n$

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Example Question #3 : How To Multiply A Monomial By A Polynomial

Expand: $\displaystyle 8x(3x+7)$

Possible Answers:

$\displaystyle 24x^2 + 56x$

$\displaystyle 11x^2 + 15x$

$\displaystyle 24x + 56$

$\displaystyle 11x + 15$

$\displaystyle 24x^2 + 56$

Correct answer:

$\displaystyle 24x^2 + 56x$

Explanation:

To expand, multiply 8x by both terms in the expression (3x + 7).

8x multiplied by 3x is 24x².

8x multiplied by 7 is 56x.

Therefore, 8x(3x + 7) = 24x² + 56x.

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Example Question #2 : How To Multiply A Monomial By A Polynomial

Write $\displaystyle 4x^2(3x^2+2x+4)$ as a polynomial.

Possible Answers:

$36x^{2}$ $\displaystyle 36x^{2}$

$12x^{4}+8x^{2}+8x$ $\displaystyle 12x^{4}+8x^{2}+8x$

$7x^{4}+6x^{3}+8x^{2}$ $\displaystyle 7x^{4}+6x^{3}+8x^{2}$

$12x^{4}+8x^{3}+16x^{2}$ $\displaystyle 12x^{4}+8x^{3}+16x^{2}$

$12x^{2}+8x+16$ $\displaystyle 12x^{2}+8x+16$

Correct answer:

$12x^{4}+8x^{3}+16x^{2}$ $\displaystyle 12x^{4}+8x^{3}+16x^{2}$

Explanation:

We need to distribute the 4x² through the terms in the parentheses:

$\displaystyle 4x^2(3x^2+2x+4)=4x^2(3x^2)+4x^2(2x)+4x^2(4)$

This becomes $\displaystyle 12x^4+8x^3+16x^2$.

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Example Question #433 : Variables

Find the product: $5g(g^{2} - 4)$ $\displaystyle 5g(g^{2} - 4)$

Possible Answers:

$5g^{3}-20$ $\displaystyle 5g^{3}-20$

$5g^{3}-20g$ $\displaystyle 5g^{3}-20g$

$5g^{2}-20g$ $\displaystyle 5g^{2}-20g$

$-16g^{2}$ $\displaystyle -16g^{2}$

$5g^{2}-20$ $\displaystyle 5g^{2}-20$

Correct answer:

$5g^{3}-20g$ $\displaystyle 5g^{3}-20g$

Explanation:

$\displaystyle 5g$ times $g^{2}$ $\displaystyle g^{2}$ gives us $5g^{3}$ $\displaystyle 5g^{3}$, while $\displaystyle 5g$ times 4 gives us 20g $\displaystyle 20g$. So it equals $5g^{3}-20g$ $\displaystyle 5g^{3}-20g$.

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Example Question #24 : Simplifying Expressions

Distribute:

$4x(2x^{2}+3x-4)$ $\displaystyle 4x(2x^{2}+3x-4)$

Possible Answers:

$8x^{3}+12x^{2}-16x$ $\displaystyle 8x^{3}+12x^{2}-16x$

$8x^{3}+12x^{2}-16$ $\displaystyle 8x^{3}+12x^{2}-16$

$8x^{3}+3x^{2}-4x$ $\displaystyle 8x^{3}+3x^{2}-4x$

$8x^{3}+12x^{2}+16x$ $\displaystyle 8x^{3}+12x^{2}+16x$

$8x^{2}+12-16$ $\displaystyle 8x^{2}+12-16$

Correct answer:

$8x^{3}+12x^{2}-16x$ $\displaystyle 8x^{3}+12x^{2}-16x$

Explanation:

Be sure to distribute the $\displaystyle x$ along with its coefficient.

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Example Question #4661 : Algebra 1

Simplify the following expression.

$4x(3x^{2}+x+10)$ $\displaystyle 4x(3x^{2}+x+10)$

Possible Answers:

$11x^{2}+40x$ $\displaystyle 11x^{2}+40x$

$7x^{3}+4x^{2}+14x$ $\displaystyle 7x^{3}+4x^{2}+14x$

$12x^{2}+14x$ $\displaystyle 12x^{2}+14x$

None of the other answers

Correct answer:

Explanation:

Distribute the outside term into the parentheses.

$4x(3x^{2}+x+10)=(4x*3x^{2})+(4x *x) +(4x* 10)$ $\displaystyle 4x(3x^{2}+x+10)=(4x*3x^{2})+(4x *x) +(4x* 10)$

Simplify each distributed factor into one expression.

$12x^{3}+4x^{2}+40x$ $\displaystyle 12x^{3}+4x^{2}+40x$

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Example Question #4662 : Algebra 1

Simplify the following expression.

$5y(3y^{3}-2y+9)$ $\displaystyle 5y(3y^{3}-2y+9)$

Possible Answers:

None of the other answers.

$8y^{4}+3y^{2}+14y$ $\displaystyle 8y^{4}+3y^{2}+14y$

$15y^{3}+35y$ $\displaystyle 15y^{3}+35y$

$8y^{4}-7y^{2}+14y$ $\displaystyle 8y^{4}-7y^{2}+14y$

Correct answer:

Explanation:

Distribute the outside term into the parentheses.

$5y(3y^{3}-2y+9)=(5y* 3y^{3})- (5y* 2y) + (5y*9)$ $\displaystyle 5y(3y^{3}-2y+9)=(5y* 3y^{3})- (5y* 2y) + (5y*9)$

Simplify each distributed factor into one expression.

$15y^{4}-10y^{2}+45y$ $\displaystyle 15y^{4}-10y^{2}+45y$

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Example Question #21 : Intermediate Single Variable Algebra

$\textup{What is the product of }2x\textup{ and }3x^{2}-5x+2\textup{?}$ $\displaystyle \textup{What is the product of }2x\textup{ and }3x^{2}-5x+2\textup{?}$

Possible Answers:

$6x^{3}+10x^{2}+4x$ $\displaystyle 6x^{3}+10x^{2}+4x$

$3x^{3}-3x^{2}+2x$ $\displaystyle 3x^{3}-3x^{2}+2x$

$6x^{3}-10x^{2}+4x$ $\displaystyle 6x^{3}-10x^{2}+4x$

$3x^{2}-10x^{2}+2$ $\displaystyle 3x^{2}-10x^{2}+2$

$6x^{2}-10x+4$ $\displaystyle 6x^{2}-10x+4$

Correct answer:

$6x^{3}-10x^{2}+4x$ $\displaystyle 6x^{3}-10x^{2}+4x$

Explanation:

$\textup{Distribute: Multiply each term in the polynomial by }2x:$ $\displaystyle \textup{Distribute: Multiply each term in the polynomial by }2x:$

$2x\left ( 3x^{2}-5x+2\right )=2x(3x^{2})+2x(-5x)+2x(2)$ $\displaystyle 2x\left ( 3x^{2}-5x+2\right )=2x(3x^{2})+2x(-5x)+2x(2)$

$6x^{3}-10x^{2}+4x$ $\displaystyle 6x^{3}-10x^{2}+4x$

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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #6 : Monomials

Example Question #2 : How To Multiply A Monomial By A Polynomial

Example Question #1 : Simplifying Expressions

Example Question #3 : How To Multiply A Monomial By A Polynomial

Example Question #2 : How To Multiply A Monomial By A Polynomial

Example Question #433 : Variables

Example Question #24 : Simplifying Expressions

Example Question #4661 : Algebra 1

Example Question #4662 : Algebra 1

Example Question #21 : Intermediate Single Variable Algebra

All Algebra 1 Resources

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