Solve 3(8-x)^2-3(x+1)(2-x)

$$3 ( 8 - x ) ^ { 2 } - 3 ( x + 1 ) ( 2 - x )$$

Evaluate

$$6x^{2}-51x+186$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(8-x\right)^{2}.

$$3\left(64-16x+x^{2}\right)-3\left(x+1\right)\left(2-x\right)$$

Use the distributive property to multiply 3 by 64-16x+x^{2}.

$$192-48x+3x^{2}-3\left(x+1\right)\left(2-x\right)$$

Use the distributive property to multiply -3 by x+1.

$$192-48x+3x^{2}+\left(-3x-3\right)\left(2-x\right)$$

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

$$192-48x+3x^{2}-3x+3x^{2}-6$$

Combine -48x and -3x to get -51x.

$$192-51x+3x^{2}+3x^{2}-6$$

Combine 3x^{2} and 3x^{2} to get 6x^{2}.

$$192-51x+6x^{2}-6$$

Subtract 6 from 192 to get 186.

$$186-51x+6x^{2}$$

Expand

$$6x^{2}-51x+186$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(8-x\right)^{2}.

$$3\left(64-16x+x^{2}\right)-3\left(x+1\right)\left(2-x\right)$$

Use the distributive property to multiply 3 by 64-16x+x^{2}.

$$192-48x+3x^{2}-3\left(x+1\right)\left(2-x\right)$$

Use the distributive property to multiply -3 by x+1.

$$192-48x+3x^{2}+\left(-3x-3\right)\left(2-x\right)$$

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

$$192-48x+3x^{2}-3x+3x^{2}-6$$

Combine -48x and -3x to get -51x.

$$192-51x+3x^{2}+3x^{2}-6$$

Combine 3x^{2} and 3x^{2} to get 6x^{2}.

$$192-51x+6x^{2}-6$$

Subtract 6 from 192 to get 186.

$$186-51x+6x^{2}$$