Solve (3x^2+5x)(3x^2-5x)

$$( 3 x ^ { 2 } + 5 x ) ( 3 x ^ { 2 } - 5 x )$$

Evaluate

$$x^{2}\left(9x^{2}-25\right)$$

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}.

$$\left(3x^{2}\right)^{2}-\left(5x\right)^{2}$$

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

$$3^{2}\left(x^{2}\right)^{2}-\left(5x\right)^{2}$$

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

$$3^{2}x^{4}-\left(5x\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{4}-\left(5x\right)^{2}$$

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

$$9x^{4}-5^{2}x^{2}$$

Calculate 5 to the power of 2 and get 25.

$$9x^{4}-25x^{2}$$

Expand

$$9x^{4}-25x^{2}$$

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}.

$$\left(3x^{2}\right)^{2}-\left(5x\right)^{2}$$

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

$$3^{2}\left(x^{2}\right)^{2}-\left(5x\right)^{2}$$

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

$$3^{2}x^{4}-\left(5x\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{4}-\left(5x\right)^{2}$$

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

$$9x^{4}-5^{2}x^{2}$$

Calculate 5 to the power of 2 and get 25.

$$9x^{4}-25x^{2}$$