Solve (6x^3+5x^2)(6x^3+5x^2)

$$(6 { x }^{ 3 } +5 { x }^{ 2 } )(6 { x }^{ 3 } +5 { x }^{ 2 } )$$

Evaluate

$$\left(6x+5\right)^{2}x^{4}$$

Solution Steps

Multiply 6x^{3}+5x^{2} and 6x^{3}+5x^{2} to get \left(6x^{3}+5x^{2}\right)^{2}.

$$\left(6x^{3}+5x^{2}\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(6x^{3}+5x^{2}\right)^{2}.

$$36\left(x^{3}\right)^{2}+60x^{3}x^{2}+25\left(x^{2}\right)^{2}$$

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

$$36x^{6}+60x^{3}x^{2}+25\left(x^{2}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$36x^{6}+60x^{5}+25\left(x^{2}\right)^{2}$$

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

$$36x^{6}+60x^{5}+25x^{4}$$

Expand

$$36x^{6}+60x^{5}+25x^{4}$$

Solution Steps

Multiply 6x^{3}+5x^{2} and 6x^{3}+5x^{2} to get \left(6x^{3}+5x^{2}\right)^{2}.

$$\left(6x^{3}+5x^{2}\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(6x^{3}+5x^{2}\right)^{2}.

$$36\left(x^{3}\right)^{2}+60x^{3}x^{2}+25\left(x^{2}\right)^{2}$$

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

$$36x^{6}+60x^{3}x^{2}+25\left(x^{2}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$36x^{6}+60x^{5}+25\left(x^{2}\right)^{2}$$

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

$$36x^{6}+60x^{5}+25x^{4}$$