Solve (x-5)(x+5)(x^2+25)

$$( x - 5 ) ( x + 5 ) ( x ^ { 2 } + 25 )$$

Evaluate

$$x^{4}-625$$

Solution Steps

Use the distributive property to multiply x-5 by x+5 and combine like terms.

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

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 25.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$x^{4}-625$$

Expand

$$x^{4}-625$$

Solution Steps

Use the distributive property to multiply x-5 by x+5 and combine like terms.

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

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 25.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$x^{4}-625$$