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

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

Evaluate

$$\left(7-x\right)\left(5x+1\right)$$

Solution Steps

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

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

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

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

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

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

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

$$4x^{2}+16x+16-9x^{2}+18x-9$$

Combine 4x^{2} and -9x^{2} to get -5x^{2}.

$$-5x^{2}+16x+16+18x-9$$

Combine 16x and 18x to get 34x.

$$-5x^{2}+34x+16-9$$

Subtract 9 from 16 to get 7.

$$-5x^{2}+34x+7$$

Expand

$$7+34x-5x^{2}$$

Solution Steps

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

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

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

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

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

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

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

$$4x^{2}+16x+16-9x^{2}+18x-9$$

Combine 4x^{2} and -9x^{2} to get -5x^{2}.

$$-5x^{2}+16x+16+18x-9$$

Combine 16x and 18x to get 34x.

$$-5x^{2}+34x+16-9$$

Subtract 9 from 16 to get 7.

$$-5x^{2}+34x+7$$