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Algebra 1 : Variables

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Example Questions

Example Question #2 : Simplifying Expressions

Find the product:

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

Possible Answers:

$\small 56n^2-14n$

$\small n^2+14$

$\small n^2-14n$

$\small n-14$

Correct answer:

$\small 56n^2-14n$

Explanation:

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

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

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

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

Add the terms together:

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

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Example Question #6 : Monomials

Expand: 8x(3x+7)

Possible Answers:

11x^2 + 15x

11x + 15

24x^2 + 56

24x^2 + 56x

24x + 56

Correct answer:

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 #7 : Monomials

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

Possible Answers:

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

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

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

$36x^{2}$

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

Correct answer:

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

Explanation:

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

4x^2(3x^2+2x+4)=4x^2(3x^2)+4x^2(2x)+4x^2(4)

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

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Example Question #112 : Basic Single Variable Algebra

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

Possible Answers:

$5g^{2}-20$

$5g^{3}-20$

$-16g^{2}$

$5g^{2}-20g$

$5g^{3}-20g$

Correct answer:

$5g^{3}-20g$

Explanation:

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

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Example Question #72 : Expressions

Distribute:

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Be sure to distribute the along with its coefficient.

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Example Question #124 : Basic Single Variable Algebra

Simplify the following expression.

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

Possible Answers:

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

$11x^{2}+40x$

None of the other answers

$12x^{2}+14x$

Correct answer:

Explanation:

Distribute the outside term into the parentheses.

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

Simplify each distributed factor into one expression.

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

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Example Question #81 : Expressions

Simplify the following expression.

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

Possible Answers:

$15y^{3}+35y$

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

None of the other answers.

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

Correct answer:

Explanation:

Distribute the outside term into the parentheses.

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

Simplify each distributed factor into one expression.

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

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Example Question #11 : How To Multiply A Monomial By A Polynomial

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

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

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Example Question #24 : Polynomials

$4x^{2}y\left ( 2xy + 6xy^{2} + 3y^{{3}}\right ) =$

Possible Answers:

$8x^{3}y^{2} + 24x^{2}y^{2} + 12x^{3}$

$8x^{3}y^{2} + 24x^{3}y^{3} + 12x^{4}y^{2}$

$8x^{2}y^{2} + 16x^{2}y^{3} + 24x^{2}y^{4}$

$8x^{3}y^{2} + 24x^{3}y^{3} + 12x^{2}y^{4}$

$32x^{3}y^{3} + 12x^{2}y^{4}$

Correct answer:

$8x^{3}y^{2} + 24x^{3}y^{3} + 12x^{2}y^{4}$

Explanation:

Use the distributive property to obtain each term:

$4x^{2}y\left ( 2xy + 6xy^{2} + 3y^{{3}}\right ) =$

$4x^{2}y(2xy) + 4x^{2}y(6xy^{2}) + 4x^{2}y(3y^{3}) =$

$8x^{3}y^{2} + 24x^{3}y^{3} + 12x^{2}y^{4}$

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Example Question #12 : How To Multiply A Monomial By A Polynomial

3x^4(2x^2 -4x +3)

Possible Answers:

6x^6+12x^5+9x^4

9x^5-12x^4+6x^6

9x^4-12x^5+6x^6

-9x^4+12x^5+6x^6

Correct answer:

9x^4-12x^5+6x^6

Explanation:

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Algebra 1 : Variables

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #2 : Simplifying Expressions

Example Question #6 : Monomials

Example Question #7 : Monomials

Example Question #112 : Basic Single Variable Algebra

Example Question #72 : Expressions

Example Question #124 : Basic Single Variable Algebra

Example Question #81 : Expressions

Example Question #11 : How To Multiply A Monomial By A Polynomial

Example Question #24 : Polynomials

Example Question #12 : How To Multiply A Monomial By A Polynomial

All Algebra 1 Resources

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