Solve 16(x-3)^2-42(3-x)^2=

$$16 ( x - 3 ) ^ { 2 } - 42 ( 3 - x ) ^ { 2 } =$$

Evaluate

$$-26\left(3-x\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$16\left(x^{2}-6x+9\right)-42\left(3-x\right)^{2}$$

Use the distributive property to multiply 16 by x^{2}-6x+9.

$$16x^{2}-96x+144-42\left(3-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3-x\right)^{2}.

$$16x^{2}-96x+144-42\left(9-6x+x^{2}\right)$$

Use the distributive property to multiply -42 by 9-6x+x^{2}.

$$16x^{2}-96x+144-378+252x-42x^{2}$$

Subtract 378 from 144 to get -234.

$$16x^{2}-96x-234+252x-42x^{2}$$

Combine -96x and 252x to get 156x.

$$16x^{2}+156x-234-42x^{2}$$

Combine 16x^{2} and -42x^{2} to get -26x^{2}.

$$-26x^{2}+156x-234$$

Expand

$$-26x^{2}+156x-234$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$16\left(x^{2}-6x+9\right)-42\left(3-x\right)^{2}$$

Use the distributive property to multiply 16 by x^{2}-6x+9.

$$16x^{2}-96x+144-42\left(3-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3-x\right)^{2}.

$$16x^{2}-96x+144-42\left(9-6x+x^{2}\right)$$

Use the distributive property to multiply -42 by 9-6x+x^{2}.

$$16x^{2}-96x+144-378+252x-42x^{2}$$

Subtract 378 from 144 to get -234.

$$16x^{2}-96x-234+252x-42x^{2}$$

Combine -96x and 252x to get 156x.

$$16x^{2}+156x-234-42x^{2}$$

Combine 16x^{2} and -42x^{2} to get -26x^{2}.

$$-26x^{2}+156x-234$$