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

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

Evaluate

$$625x^{4}-y^{4}$$

Solution Steps

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

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

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

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

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

$$\left(25x^{2}\right)^{2}-y^{4}$$

Expand \left(25x^{2}\right)^{2}.

$$25^{2}\left(x^{2}\right)^{2}-y^{4}$$

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

$$25^{2}x^{4}-y^{4}$$

Calculate 25 to the power of 2 and get 625.

$$625x^{4}-y^{4}$$

Expand

$$625x^{4}-y^{4}$$

Solution Steps

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

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

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

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

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

$$\left(25x^{2}\right)^{2}-y^{4}$$

Expand \left(25x^{2}\right)^{2}.

$$25^{2}\left(x^{2}\right)^{2}-y^{4}$$

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

$$25^{2}x^{4}-y^{4}$$

Calculate 25 to the power of 2 and get 625.

$$625x^{4}-y^{4}$$