# Simplify (x^2+6x+5)(2x^2-8x+7)

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Multiply each term in the first polynomial by each term in the second polynomial.

`(x^2 * 2x^2 + x^2 * - 8x + x^2 * 7 + 6x * 2x^2 + 6x * -8x + 6x * 7 + 5 * 2x^2 + 5 * -8x + 5 * 7)`

Multiply each term in the first polynomial by each term in the second polynomial.

`(2x^4 + 4x^3 - 31x^2 + 2x + 35)`

Remove the parentheses around the expression `2x^4 + 4x^3 - 31x^2 + 2x + 35`

Therefore, the answer is

`2x^4 + 4x^3 - 31x^2 + 2x + 35`

The product (x^2+6x+5)(2x^2-8x+7) has to be determined.

(x^2+6x+5)(2x^2-8x+7)

= x^2*(2x^2-8x+7)+6x*(2x^2-8x+7)+5*(2x^2-8x+7)

= 4x^4 - 8x^3 + 7x^2 + 12x^3 - 48x^2 +42x + 10x^2 - 40x + 35

= 4x^4 + 4x^3 - 31x^2 + 2x + 35

**The product (x^2+6x+5)(2x^2-8x+7) = 4x^4 + 4x^3 - 31x^2 + 2x + 35**

To simplify (x^2+6x+5)(2x^2-8x+7), the product has to be determined as a polynomial.

(x^2+6x+5)(2x^2-8x+7)

= x^2*(2x^2-8x+7) + 6*x*(2x^2-8x+7) + 5*(2x^2-8x+7)

= 2x^2*x^2 - 8x*x^2 + 7*x^2 + 12x^3 - 48x^2 + 42x + 10x^2 - 40x + 35

= 2x^4 - 8x^3 + 7x^2 + 12x^3 - 48x^2 + 42x + 10x^2 - 40x + 35

= 2x^4 - 8x^3 + 12x^3 + 7x^2 - 48x^2 + 10x^2 + 42x - 40x + 35

= 2x^4 + 4x^3 -31x^2 + 2x + 35

`(x^2 + 6x + 5 )( 2x^2 - 8x + 7)`

To simplify this apply the distributive law,

`(x^2*2x^2 + x^2*-8x + x^2*7 + 6x*2x^2 + 6x*-8x + 6x*7 + 5*2x^2 + 5*-8x + 5*7)`

`(2x^4 - 8x^3 + 7x^2 + 12x^3 - 48x^2 + 42x + 10x^2 - 40x + 35)`

Arrange them

`(2x^4 - 8x^3 + 12x^3 + 7x^2 - 48x^2 + 10x^2 + 42x - 40x + 35)`

`2x^4 + 4x^3 - 31x^2 + 2x + 35 Answer.`