To multiply the expressions \((-8x + 5)(2x - 7)\), follow these steps:
1. Apply the distributive property (FOIL Method):
- First terms: Multiply the first terms in each binomial: \((-8x) \cdot (2x) = -16x^2\)
- Outer terms: Multiply the outer terms in the expression: \((-8x) \cdot (-7) = 56x\)
- Inner terms: Multiply the inner terms in the expression: \(5 \cdot (2x) = 10x\)
- Last terms: Multiply the last terms in each binomial: \(5 \cdot (-7) = -35\)
2. Combine all these products:
[tex]\[
-16x^2 + 56x + 10x - 35
\][/tex]
3. Simplify by combining like terms:
- Combine \(56x\) and \(10x\):
[tex]\[
56x + 10x = 66x
\][/tex]
Therefore, the final simplified expression is:
[tex]\[
-16x^2 + 66x - 35
\][/tex]
Thus, [tex]\((-8x + 5)(2x - 7) = -16x^2 + 66x - 35\)[/tex].
