Solve x^2-(7-3x)^2

$$x ^ { 2 } - ( 7 - 3 x ) ^ { 2 }$$

Evaluate

$$\left(7-2x\right)\left(4x-7\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(7-3x\right)^{2}.

$$x^{2}-\left(49-42x+9x^{2}\right)$$

To find the opposite of 49-42x+9x^{2}, find the opposite of each term.

$$x^{2}-49+42x-9x^{2}$$

Combine x^{2} and -9x^{2} to get -8x^{2}.

$$-8x^{2}-49+42x$$

Expand

$$-8x^{2}+42x-49$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(7-3x\right)^{2}.

$$x^{2}-\left(49-42x+9x^{2}\right)$$

To find the opposite of 49-42x+9x^{2}, find the opposite of each term.

$$x^{2}-49+42x-9x^{2}$$

Combine x^{2} and -9x^{2} to get -8x^{2}.

$$-8x^{2}-49+42x$$