Question

1. use the distributive property to multiply the trinomial by the binomial.

circle the first term in the trinomial, multiply it by each term in the binomial, and place each result in the blank spaces provided. repeat this process for the second and third terms of the trinomial until all of the spaces are filled in. finally, in the space provided beneath the blanks, simplify the expression by combining like terms and arranging the terms from highest to lowest order. show your work. (4 points)
(3x² - 2x + 7)(x² + 2x)
__ + + + + + __

Explanation:

Step1: Multiply \(3x^{2}\) by each term in \((x^{2}+2x)\)

\(3x^{2}\times x^{2}=3x^{4}\), \(3x^{2}\times2x = 6x^{3}\)

Step2: Multiply \(-2x\) by each term in \((x^{2}+2x)\)

\(-2x\times x^{2}=-2x^{3}\), \(-2x\times2x=-4x^{2}\)

Step3: Multiply \(7\) by each term in \((x^{2}+2x)\)

\(7\times x^{2}=7x^{2}\), \(7\times2x = 14x\)

Step4: Combine like terms

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Answer:

\(3x^{4}+4x^{3}+3x^{2}+14x\)