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

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

Evaluate

$$-77x^{2}-170x-77$$

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 -77x^{2}.

$$-77x^{2}-8x+4-162x-81$$

Combine -8x and -162x to get -170x.

$$-77x^{2}-170x+4-81$$

Subtract 81 from 4 to get -77.

$$-77x^{2}-170x-77$$

Expand

$$-77x^{2}-170x-77$$

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 -77x^{2}.

$$-77x^{2}-8x+4-162x-81$$

Combine -8x and -162x to get -170x.

$$-77x^{2}-170x+4-81$$

Subtract 81 from 4 to get -77.

$$-77x^{2}-170x-77$$