Solve (4w^2+7z^3)(4w^2-7z^3)=

$$( 4 w ^ { 2 } + 7 z ^ { 3 } ) ( 4 w ^ { 2 } - 7 z ^ { 3 } ) =$$

Evaluate

$$16w^{4}-49z^{6}$$

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}.

$$\left(4w^{2}\right)^{2}-\left(7z^{3}\right)^{2}$$

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

$$4^{2}\left(w^{2}\right)^{2}-\left(7z^{3}\right)^{2}$$

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

$$4^{2}w^{4}-\left(7z^{3}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16w^{4}-\left(7z^{3}\right)^{2}$$

Expand \left(7z^{3}\right)^{2}.

$$16w^{4}-7^{2}\left(z^{3}\right)^{2}$$

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

$$16w^{4}-7^{2}z^{6}$$

Calculate 7 to the power of 2 and get 49.

$$16w^{4}-49z^{6}$$

Expand

$$16w^{4}-49z^{6}$$

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}.

$$\left(4w^{2}\right)^{2}-\left(7z^{3}\right)^{2}$$

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

$$4^{2}\left(w^{2}\right)^{2}-\left(7z^{3}\right)^{2}$$

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

$$4^{2}w^{4}-\left(7z^{3}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16w^{4}-\left(7z^{3}\right)^{2}$$

Expand \left(7z^{3}\right)^{2}.

$$16w^{4}-7^{2}\left(z^{3}\right)^{2}$$

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

$$16w^{4}-7^{2}z^{6}$$

Calculate 7 to the power of 2 and get 49.

$$16w^{4}-49z^{6}$$