Solve 400^2-256x^2

$$400 ^ { 2 } - 256 x ^ { 2 }$$

Factor

$$256\left(-x-25\right)\left(x-25\right)$$

Solution Steps

Factor out 256.

$$256\left(625-x^{2}\right)$$

Consider 625-x^{2}. Rewrite 625-x^{2} as 25^{2}-x^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(25-x\right)\left(25+x\right)$$

Reorder the terms.

$$\left(-x+25\right)\left(x+25\right)$$

Rewrite the complete factored expression.

$$256\left(-x+25\right)\left(x+25\right)$$

Evaluate

$$160000-256x^{2}$$

Solution Steps

Calculate 400 to the power of 2 and get 160000.

$$160000-256x^{2}$$