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PSAT Math : How to multiply a monomial by a polynomial

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Example Questions

Example Question #1 : Monomials

If you have a rectangle with a width of and a length of 7n-3y +2 , what is the area of the rectangle?

Possible Answers:

$14ny^{3}$

$21n^{2}-9ny+6n$

$56n^{2}-27ny+18n$

21ny-9ny+2ny

$21n-9y^{2}+6$

Correct answer:

$21n^{2}-9ny+6n$

Explanation:

To find the area of a rectangle, multiply the length times the width. Therefore, you must multiply times 7n-3y +2 . To do that, you must multiply the monomial times each part of the trinomial, like so:

7n(3n)-3y(3n) +2(3n)

21n^2-9ny+6n

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Example Question #2 : Monomials

Find the product:

6x^3y^5(3x^2z^4+x^3y+7y)

Possible Answers:

6x^3y^5z^4+6x^3y^5+7y^6

9x^5y^6+6x^3y^6+7

18x^6y^5z^4+6x^9y^5+42x^3y^5

18x^5y^5z^4 + 6x^6y^6+42x^3y^6

Correct answer:

18x^5y^5z^4 + 6x^6y^6+42x^3y^6

Explanation:

Use the distributive property:

6x^3y^5(3x^2z^4+x^3y+7y)

(6x^3y^5)(3x^2z^4)+(6x^3y^5)(x^3y)+(6x^3y^5)(7y)

Simplify: don't forget to use the rules of multiplying exponents (add them)

18x^5y^5z^4 + 6x^6y^6+42x^3y^6

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Example Question #3 : Monomials

Find the product:

4a^2(ab^2+a^2b+ac^3)

Possible Answers:

4a^2b^2+4a^4b+4a^2b^3

4ab^3+4a^2b^3+4ac

4a^2b^3+4ab

4a^3b^2+4a^4b+4a^3b^3

8a^2b^2+4a^4b

Correct answer:

4a^3b^2+4a^4b+4a^3b^3

Explanation:

Find the product:

4a^2(ab^2+a^2b+ac^3)

Use the distributive property:

$(4a^2\cdot ab^2)+(4a^2\cdot a^2b)+(4a^2\cdot ac^3)$

When multiplying variables with exponents, add the exponents:

4a^3b^2+4a^4b+4a^3c^3

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Example Question #3 : Monomials

Find the product:

5x^3(x^2+2x+4)

Possible Answers:

5x^5+10x^4+20x^3

5x^6+30x^3

5x^2+2.5x^2+1.25x^3

5x^6+10x^4+20x^3

5x^3+x^2+2x+4

Correct answer:

5x^5+10x^4+20x^3

Explanation:

Find the product:

5x^3(x^2+2x+4)

Use the distributive property:

$(5x^3 \cdot x^2)+(5x^3 \cdot 2x)+(5x^3 \cdot 4)$

5x^5+10x^4+20x^3

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PSAT Math : How to multiply a monomial by a polynomial

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : Monomials

Example Question #2 : Monomials

Example Question #3 : Monomials

Example Question #3 : Monomials

All PSAT Math Resources

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