the formula for the area of a parallelogram is ( a = bh ), where ( b ) is the base and ( h ) is the height…

the formula for the area of a parallelogram is ( a = bh ), where ( b ) is the base and ( h ) is the height. which simplified expression represents the area of the parallelogram? ( -4x^{3}+14x - 24 ) square centimeters ( 2x^{3}-6x^{2}-14x + 24 ) square centimeters ( -4x^{3}-14x + 24 ) square centimeters ( 2x^{3}+6x^{2}+14x + 24 ) square centimeters

the formula for the area of a parallelogram is ( a = bh ), where ( b ) is the base and ( h ) is the height. which simplified expression represents the area of the parallelogram? ( -4x^{3}+14x - 24 ) square centimeters ( 2x^{3}-6x^{2}-14x + 24 ) square centimeters ( -4x^{3}-14x + 24 ) square centimeters ( 2x^{3}+6x^{2}+14x + 24 ) square centimeters

Answer

Explanation:

Step1: Substitute (b = 2x^{2}+2x - 6) and (h=x - 4) into (A=bh)

[A=(2x^{2}+2x - 6)(x - 4)]

Step2: Use the distributive property (FOIL for polynomials)

[ \begin{align*} A&=2x^{2}(x-4)+2x(x - 4)-6(x - 4)\ &=2x^{3}-8x^{2}+2x^{2}-8x-6x + 24 \end{align*} ]

Step3: Combine like - terms

[ \begin{align*} A&=2x^{3}+(-8x^{2}+2x^{2})+(-8x-6x)+24\ &=2x^{3}-6x^{2}-14x + 24 \end{align*} ]

Answer:

(2x^{3}-6x^{2}-14x + 24) square centimeters (the second option)