Questions: Multiply and simplify (5x^2 - 8x - 1)(2x^2 - 7x + 8)

Multiply and simplify (5x^2 - 8x - 1)(2x^2 - 7x + 8)
Transcript text: Multiply and simplify $\left(5 x^{2}-8 x-1\right)\left(2 x^{2}-7 x+8\right)$
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Solution

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Solution Steps

To solve the problem of multiplying and simplifying the given polynomials \((5x^2 - 8x - 1)(2x^2 - 7x + 8)\), we will use the distributive property (also known as the FOIL method for binomials) to expand the expression and then combine like terms.

Step 1: Multiply the Polynomials

We start with the polynomials \( (5x^2 - 8x - 1) \) and \( (2x^2 - 7x + 8) \). Using the distributive property, we multiply each term in the first polynomial by each term in the second polynomial.

Step 2: Combine Like Terms

After performing the multiplication, we combine like terms to simplify the expression. The result of the multiplication is:

\[ 10x^4 - 51x^3 + 94x^2 - 57x - 8 \]

Final Answer

The simplified expression is

\[ \boxed{10x^4 - 51x^3 + 94x^2 - 57x - 8} \]

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