Solve (8x^3-6y)(8x^3+6y

$$( 8 x ^ { 3 } - 6 y ) ( 8 x ^ { 3 } + 6 y$$

Evaluate

$$64x^{6}-36y^{2}$$

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}.

$$\left(8x^{3}\right)^{2}-\left(6y\right)^{2}$$

Expand \left(8x^{3}\right)^{2}.

$$8^{2}\left(x^{3}\right)^{2}-\left(6y\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$8^{2}x^{6}-\left(6y\right)^{2}$$

Calculate 8 to the power of 2 and get 64.

$$64x^{6}-\left(6y\right)^{2}$$

Expand \left(6y\right)^{2}.

$$64x^{6}-6^{2}y^{2}$$

Calculate 6 to the power of 2 and get 36.

$$64x^{6}-36y^{2}$$

Expand

$$64x^{6}-36y^{2}$$

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}.

$$\left(8x^{3}\right)^{2}-\left(6y\right)^{2}$$

Expand \left(8x^{3}\right)^{2}.

$$8^{2}\left(x^{3}\right)^{2}-\left(6y\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$8^{2}x^{6}-\left(6y\right)^{2}$$

Calculate 8 to the power of 2 and get 64.

$$64x^{6}-\left(6y\right)^{2}$$

Expand \left(6y\right)^{2}.

$$64x^{6}-6^{2}y^{2}$$

Calculate 6 to the power of 2 and get 36.

$$64x^{6}-36y^{2}$$