Solve -4left(x-1right)^2-81left(x+1right)^2

$$-4 { \left(x-1 \right) }^{ 2 } -81 { \left(x+1 \right) }^{ 2 }$$

Evaluate

$$-85x^{2}-154x-85$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$-4\left(x^{2}-2x+1\right)-81\left(x+1\right)^{2}$$

Use the distributive property to multiply -4 by x^{2}-2x+1.

$$-4x^{2}+8x-4-81\left(x+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$-4x^{2}+8x-4-81\left(x^{2}+2x+1\right)$$

Use the distributive property to multiply -81 by x^{2}+2x+1.

$$-4x^{2}+8x-4-81x^{2}-162x-81$$

Combine -4x^{2} and -81x^{2} to get -85x^{2}.

$$-85x^{2}+8x-4-162x-81$$

Combine 8x and -162x to get -154x.

$$-85x^{2}-154x-4-81$$

Subtract 81 from -4 to get -85.

$$-85x^{2}-154x-85$$

Expand

$$-85x^{2}-154x-85$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$-4\left(x^{2}-2x+1\right)-81\left(x+1\right)^{2}$$

Use the distributive property to multiply -4 by x^{2}-2x+1.

$$-4x^{2}+8x-4-81\left(x+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$-4x^{2}+8x-4-81\left(x^{2}+2x+1\right)$$

Use the distributive property to multiply -81 by x^{2}+2x+1.

$$-4x^{2}+8x-4-81x^{2}-162x-81$$

Combine -4x^{2} and -81x^{2} to get -85x^{2}.

$$-85x^{2}+8x-4-162x-81$$

Combine 8x and -162x to get -154x.

$$-85x^{2}-154x-4-81$$

Subtract 81 from -4 to get -85.

$$-85x^{2}-154x-85$$