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

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

Evaluate

$$x^{2}-28x+99$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5\right)^{2}.

$$3\left(x^{2}-10x+25\right)-2\left(x+3\right)\left(x-4\right)$$

Use the distributive property to multiply 3 by x^{2}-10x+25.

$$3x^{2}-30x+75-2\left(x+3\right)\left(x-4\right)$$

Use the distributive property to multiply -2 by x+3.

$$3x^{2}-30x+75+\left(-2x-6\right)\left(x-4\right)$$

Use the distributive property to multiply -2x-6 by x-4 and combine like terms.

$$3x^{2}-30x+75-2x^{2}+2x+24$$

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

$$x^{2}-30x+75+2x+24$$

Combine -30x and 2x to get -28x.

$$x^{2}-28x+75+24$$

Add 75 and 24 to get 99.

$$x^{2}-28x+99$$

Expand

$$x^{2}-28x+99$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5\right)^{2}.

$$3\left(x^{2}-10x+25\right)-2\left(x+3\right)\left(x-4\right)$$

Use the distributive property to multiply 3 by x^{2}-10x+25.

$$3x^{2}-30x+75-2\left(x+3\right)\left(x-4\right)$$

Use the distributive property to multiply -2 by x+3.

$$3x^{2}-30x+75+\left(-2x-6\right)\left(x-4\right)$$

Use the distributive property to multiply -2x-6 by x-4 and combine like terms.

$$3x^{2}-30x+75-2x^{2}+2x+24$$

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

$$x^{2}-30x+75+2x+24$$

Combine -30x and 2x to get -28x.

$$x^{2}-28x+75+24$$

Add 75 and 24 to get 99.

$$x^{2}-28x+99$$