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Algebra 1 : How to multiply trinomials

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Example Questions

Example Question #31 : Polynomials

Multiply: $\displaystyle (x^2+x-1)(x^2-2x-1)$

Possible Answers:

$\displaystyle x^4+x^3-4x^2-x+1$

$\displaystyle x^4+x^3-4x^2+x+1$

$\displaystyle x^4+x^3+4x^2-x+1$

$\displaystyle x^4-x^3-4x^2+x+1$

$\displaystyle x^4-x^3+4x^2+x+1$

Correct answer:

$\displaystyle x^4-x^3-4x^2+x+1$

Explanation:

In order to solve, we will need to multiply each term of the first trinomial with all the terms of the second trinomial. Sum all the terms together.

$\displaystyle x^2(x^2-2x-1) = x^4-2x^3-x^2$

$\displaystyle x(x^2-2x-1)= x^3-2x^2-x$

$\displaystyle -1(x^2-2x-1) = -x^2+2x+1$

Add all of the terms and combine like terms.

$\displaystyle x^4-2x^3-x^2+(x^3-2x^2-x)+(-x^2+2x+1)$

The answer is: $\displaystyle x^4-x^3-4x^2+x+1$

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Example Question #32 : Polynomials

Multiply: $\displaystyle (3x^2-2x+4)(x^2+x-5)$

Possible Answers:

$\displaystyle 3x^4+x^3-13x^2+14x-20$

$\displaystyle 3x^4-x^3-13x^2+14x-20$

$\displaystyle 3x^4-8x^3-17x^2+6x-20$

$\displaystyle 3x^4-x^3+13x^2-14x-20$

$\displaystyle 3x^4-5x^3-9x^2+6x-20$

Correct answer:

$\displaystyle 3x^4+x^3-13x^2+14x-20$

Explanation:

Multiply each term of the first trinomial with the terms of the second trinomial.

$\displaystyle 3x^2(x^2+x-5) = 3x^4+3x^3-15x^2$

$\displaystyle -2x(x^2+x-5) = -2x^3-2x^2+10x$

$\displaystyle 4(x^2+x-5) = 4x^2+4x-20$

Combine like-terms.

$\displaystyle 3x^4+3x^3-15x^2+(-2x^3-2x^2+10x)+(4x^2+4x-20)$

The answer is: $\displaystyle 3x^4+x^3-13x^2+14x-20$

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Algebra 1 : How to multiply trinomials

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #31 : Polynomials

Example Question #32 : Polynomials

All Algebra 1 Resources

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