Answer:
5x^4 -37x^3 -6x^2 +41x -6
Step-by-step explanation:
We simplify this expression by removing parentheses and combining like terms. Parentheses are removed using the distributive property.
Form the product
The product of the final pair of polynomials in parentheses is ...
(-4x^3 +5x -1)(2x -7) = (-4x^3 +5x -1)(2x) +(-4x^3 +5x -1)(-7)
= -8x^4 +10x^2 -2x +28x^3 -35x +7
= -8x^4 +28x^3 +10x^2 -37x +7
Combine with remaining sums
= (5x^4 -9x^3 +7x -1) + (-8x^4 +4x^2 -3x +2) - (-8x^4 +28x^3 +10x^2 -37x +7)
= (5 -8 -(-8))x^4 +(-9 -28)x^3 +(4 -10)x^2 +(7 -3 -(-37))x +(-1 +2 -7)
= 5x^4 -37x^3 -6x^2 +41x -6
