Solve (4x+5y^4)(4x-5y^4)

$$( 4 x + 5 y ^ { 4 } ) ( 4 x - 5 y ^ { 4 } )$$

Evaluate

$$16x^{2}-25y^{8}$$

Solution Steps

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

$$\left(4x\right)^{2}-\left(5y^{4}\right)^{2}$$

Expand \left(4x\right)^{2}.

$$4^{2}x^{2}-\left(5y^{4}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16x^{2}-\left(5y^{4}\right)^{2}$$

Expand \left(5y^{4}\right)^{2}.

$$16x^{2}-5^{2}\left(y^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$16x^{2}-5^{2}y^{8}$$

Calculate 5 to the power of 2 and get 25.

$$16x^{2}-25y^{8}$$

Expand

$$16x^{2}-25y^{8}$$

Solution Steps

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

$$\left(4x\right)^{2}-\left(5y^{4}\right)^{2}$$

Expand \left(4x\right)^{2}.

$$4^{2}x^{2}-\left(5y^{4}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16x^{2}-\left(5y^{4}\right)^{2}$$

Expand \left(5y^{4}\right)^{2}.

$$16x^{2}-5^{2}\left(y^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$16x^{2}-5^{2}y^{8}$$

Calculate 5 to the power of 2 and get 25.

$$16x^{2}-25y^{8}$$