Solve 4(x+1)^2-2(x-2)(x-3)-5x=

$$4 ( x + 1 ) ^ { 2 } - 2 ( x - 2 ) ( x - 3 ) - 5 x =$$

Evaluate

$$2x^{2}+13x-8$$

Solution Steps

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

$$4\left(x^{2}+2x+1\right)-2\left(x-2\right)\left(x-3\right)-5x$$

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

$$4x^{2}+8x+4-2\left(x-2\right)\left(x-3\right)-5x$$

Use the distributive property to multiply -2 by x-2.

$$4x^{2}+8x+4+\left(-2x+4\right)\left(x-3\right)-5x$$

Use the distributive property to multiply -2x+4 by x-3 and combine like terms.

$$4x^{2}+8x+4-2x^{2}+10x-12-5x$$

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

$$2x^{2}+8x+4+10x-12-5x$$

Combine 8x and 10x to get 18x.

$$2x^{2}+18x+4-12-5x$$

Subtract 12 from 4 to get -8.

$$2x^{2}+18x-8-5x$$

Combine 18x and -5x to get 13x.

$$2x^{2}+13x-8$$

Expand

$$2x^{2}+13x-8$$

Solution Steps

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

$$4\left(x^{2}+2x+1\right)-2\left(x-2\right)\left(x-3\right)-5x$$

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

$$4x^{2}+8x+4-2\left(x-2\right)\left(x-3\right)-5x$$

Use the distributive property to multiply -2 by x-2.

$$4x^{2}+8x+4+\left(-2x+4\right)\left(x-3\right)-5x$$

Use the distributive property to multiply -2x+4 by x-3 and combine like terms.

$$4x^{2}+8x+4-2x^{2}+10x-12-5x$$

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

$$2x^{2}+8x+4+10x-12-5x$$

Combine 8x and 10x to get 18x.

$$2x^{2}+18x+4-12-5x$$

Subtract 12 from 4 to get -8.

$$2x^{2}+18x-8-5x$$

Combine 18x and -5x to get 13x.

$$2x^{2}+13x-8$$