Solve 9(x-1)^2-4(2x+3)^2

$$9 ( x - 1 ) ^ { 2 } - 4 ( 2 x + 3 ) ^ { 2 }$$

Evaluate

$$-\left(x+9\right)\left(7x+3\right)$$

Solution Steps

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

$$9\left(x^{2}-2x+1\right)-4\left(2x+3\right)^{2}$$

Use the distributive property to multiply 9 by x^{2}-2x+1.

$$9x^{2}-18x+9-4\left(2x+3\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+3\right)^{2}.

$$9x^{2}-18x+9-4\left(4x^{2}+12x+9\right)$$

Use the distributive property to multiply -4 by 4x^{2}+12x+9.

$$9x^{2}-18x+9-16x^{2}-48x-36$$

Combine 9x^{2} and -16x^{2} to get -7x^{2}.

$$-7x^{2}-18x+9-48x-36$$

Combine -18x and -48x to get -66x.

$$-7x^{2}-66x+9-36$$

Subtract 36 from 9 to get -27.

$$-7x^{2}-66x-27$$

Expand

$$-7x^{2}-66x-27$$

Solution Steps

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

$$9\left(x^{2}-2x+1\right)-4\left(2x+3\right)^{2}$$

Use the distributive property to multiply 9 by x^{2}-2x+1.

$$9x^{2}-18x+9-4\left(2x+3\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+3\right)^{2}.

$$9x^{2}-18x+9-4\left(4x^{2}+12x+9\right)$$

Use the distributive property to multiply -4 by 4x^{2}+12x+9.

$$9x^{2}-18x+9-16x^{2}-48x-36$$

Combine 9x^{2} and -16x^{2} to get -7x^{2}.

$$-7x^{2}-18x+9-48x-36$$

Combine -18x and -48x to get -66x.

$$-7x^{2}-66x+9-36$$

Subtract 36 from 9 to get -27.

$$-7x^{2}-66x-27$$