Solve (25h^2+12h)^2

$$( 25 h ^ { 2 } + 12 h ) ^ { 2 }$$

Evaluate

$$\left(h\left(25h+12\right)\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(25h^{2}+12h\right)^{2}.

$$625\left(h^{2}\right)^{2}+600h^{2}h+144h^{2}$$

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

$$625h^{4}+600h^{2}h+144h^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$625h^{4}+600h^{3}+144h^{2}$$

Expand

$$625h^{4}+600h^{3}+144h^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(25h^{2}+12h\right)^{2}.

$$625\left(h^{2}\right)^{2}+600h^{2}h+144h^{2}$$

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

$$625h^{4}+600h^{2}h+144h^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$625h^{4}+600h^{3}+144h^{2}$$