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

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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**

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`

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