Question

Polynomial Operation Assignment*all work/steps shown or describe in wordsI need help on these

Answer 1

In each case, use the distributive property to multiply the polynomials:

5)

`\begin{gathered} (2x+7)(x^2-4x+6)=(2x+7)(x^2)+(2x+7)(-4x)+(2x+7)(6) \\ =(2x)(x^2)+(7)(x^2)+(2x)(-4x)+(7)(-4x)+(2x)(6)+(7)(6) \\ =2x^3+7x^2-8x^2-28x+12x+42 \\ =2x^3-x^2+-16x+42 \end{gathered}`

Therefore:

`(2x+7)(x^2-4x+6)=2x^3-x^2-16x+42`

6)

Therefore:

`\mleft(4x^2-2x+6\mright)\mleft(x^2+5x-1\mright)=4x^4+18x^3-8x^2+32x-6`

7)

`\begin{gathered} (2x+7)^2=(2x+7)(2x+7) \\ =(2x)(2x+7)+(7)(2x+7) \\ =(2x)(2x)+(2x)(7)+(7)(2x)+(7)(7) \\ =4x^2+14x+14x+49 \\ =4x^2+28x+49 \end{gathered}`

Therefore:

`(2x+7)^2=4x^2+28x+49`