Solve -9(x+2)^2+16(x-1)^2

$$- 9 ( x + 2 ) ^ { 2 } + 16 ( x - 1 ) ^ { 2 }$$

Evaluate

$$\left(x-10\right)\left(7x+2\right)$$

Solution Steps

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

$$-9\left(x^{2}+4x+4\right)+16\left(x-1\right)^{2}$$

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

$$-9x^{2}-36x-36+16\left(x-1\right)^{2}$$

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

$$-9x^{2}-36x-36+16\left(x^{2}-2x+1\right)$$

Use the distributive property to multiply 16 by x^{2}-2x+1.

$$-9x^{2}-36x-36+16x^{2}-32x+16$$

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

$$7x^{2}-36x-36-32x+16$$

Combine -36x and -32x to get -68x.

$$7x^{2}-68x-36+16$$

Add -36 and 16 to get -20.

$$7x^{2}-68x-20$$

Expand

$$7x^{2}-68x-20$$

Solution Steps

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

$$-9\left(x^{2}+4x+4\right)+16\left(x-1\right)^{2}$$

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

$$-9x^{2}-36x-36+16\left(x-1\right)^{2}$$

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

$$-9x^{2}-36x-36+16\left(x^{2}-2x+1\right)$$

Use the distributive property to multiply 16 by x^{2}-2x+1.

$$-9x^{2}-36x-36+16x^{2}-32x+16$$

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

$$7x^{2}-36x-36-32x+16$$

Combine -36x and -32x to get -68x.

$$7x^{2}-68x-36+16$$

Add -36 and 16 to get -20.

$$7x^{2}-68x-20$$