Solve 100^2-4^2x^4

$$100 ^ { 2 } - 4 ^ { 2 } x ^ { 4 }$$

Evaluate

$$10000-16x^{4}$$

Solution Steps

Calculate 100 to the power of 2 and get 10000.

$$10000-4^{2}x^{4}$$

Calculate 4 to the power of 2 and get 16.

$$10000-16x^{4}$$

Factor

$$16\left(x-5\right)\left(x+5\right)\left(-x^{2}-25\right)$$

Solution Steps

Factor out 16.

$$16\left(625-x^{4}\right)$$

Consider 625-x^{4}. Rewrite 625-x^{4} as 25^{2}-\left(-x^{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Reorder the terms.

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

Consider -x^{2}+25. Rewrite -x^{2}+25 as 5^{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).

$$\left(5-x\right)\left(5+x\right)$$

Reorder the terms.

$$\left(-x+5\right)\left(x+5\right)$$

Rewrite the complete factored expression. Polynomial x^{2}+25 is not factored since it does not have any rational roots.

$$16\left(x^{2}+25\right)\left(-x+5\right)\left(x+5\right)$$