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PSAT Math : How to multiply trinomials

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Example Questions

Example Question #31 : Polynomials

(x^2+y^2+z^2)(x^2+y^2+z^2)

Possible Answers:

x^4+x^2y^2+y^2z^2+z^4

x^4+y^4+z^4+2x^2y^2+2y^2z^2+2x^2z^2

2x^2y^2+z^4+y^4+2z^2y^2

x^2y^2+y^2z^2+x^2z^2

x^4+y^4+z^4

Correct answer:

x^4+y^4+z^4+2x^2y^2+2y^2z^2+2x^2z^2

Explanation:

(x^2+y^2+z^2)(x^2+y^2+z^2)

Use the distributive property:

x^2(x^2+y^2+z^2)+y^2(x^2+y^2+z^2)+z^2(x^2+y^2+z^2)

x^4+x^2y^2+x^2z^2 + x^2y^2+y^4+y^2z^2+x^2z^2+y^2z^2+z^4

Combine like terms:

x^4+y^4+z^4+2x^2y^2+2y^2z^2+2x^2z^2

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Example Question #2 : How To Multiply Trinomials

Find the product:

(x^2+7x+4)(x^2-3x-2)

Possible Answers:

2x^2+4x+2

x^4-10x^3+27x^2-14x-4

x^4-21x-8

x^4+4x^3-19x^2-26x-8

2x^2-4x-2

Correct answer:

x^4+4x^3-19x^2-26x-8

Explanation:

Find the product:

(x^2+7x+4)(x^2-3x-2)

Step 1: Use the Distributive Property

x^2(x^2-3x-2)+7x(x^2-3x-2)+4(x^2-3x-2)

x^4-3x^3-2x^2+7x^3-21x^2-14x+4x^2-12x-8

Step 2: Combine like terms

x^4+4x^3-19x^2-26x-8

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Example Question #32 : Polynomials

Find the product:

(2x^2+3y+6)(7x^2+4y+1)

Possible Answers:

21x^2y+12y^2+3y

14x^4+8x^2y+2x^2

42x^2+24y+6

14x^2+29x^2y+44x^2+12y^2+27y+6

14x^2+8x^2y+12y^2+8

Correct answer:

14x^2+29x^2y+44x^2+12y^2+27y+6

Explanation:

Find the product:

(2x^2+3y+6)(7x^2+4y+1)

Use the distributive property:

2x^2(7x^2+4y+1)+3y(7x^2+4y+1)+6(7x^2+4y+1)

14x^4+8x^2y+2x^2+21x^2y+12y^2+3y+42x^2+24y+6

14x^4+29x^2y+44x^2+12y^2+27y+6

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PSAT Math : How to multiply trinomials

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #31 : Polynomials

Example Question #2 : How To Multiply Trinomials

Example Question #32 : Polynomials

All PSAT Math Resources

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