Solve (x+4y)(x-4y)(x^2+16y^2

$$( x + 4 y ) ( x - 4 y ) ( x ^ { 2 } + 16 y ^ { 2 }$$

Evaluate

$$x^{4}-256y^{4}$$

Solution Steps

Use the distributive property to multiply x+4y by x-4y and combine like terms.

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

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

$$\left(x^{2}\right)^{2}-\left(16y^{2}\right)^{2}$$

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

$$x^{4}-\left(16y^{2}\right)^{2}$$

Expand \left(16y^{2}\right)^{2}.

$$x^{4}-16^{2}\left(y^{2}\right)^{2}$$

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

$$x^{4}-16^{2}y^{4}$$

Calculate 16 to the power of 2 and get 256.

$$x^{4}-256y^{4}$$

Expand

$$x^{4}-256y^{4}$$

Solution Steps

Use the distributive property to multiply x+4y by x-4y and combine like terms.

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

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

$$\left(x^{2}\right)^{2}-\left(16y^{2}\right)^{2}$$

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

$$x^{4}-\left(16y^{2}\right)^{2}$$

Expand \left(16y^{2}\right)^{2}.

$$x^{4}-16^{2}\left(y^{2}\right)^{2}$$

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

$$x^{4}-16^{2}y^{4}$$

Calculate 16 to the power of 2 and get 256.

$$x^{4}-256y^{4}$$