Solve e*(2x^2+4)^2

$$e \cdot ( 2 x ^ { 2 } + 4 ) ^ { 2 }$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x^{2}+4\right)^{2}.

$$e\left(4\left(x^{2}\right)^{2}+16x^{2}+16\right)$$

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

$$e\left(4x^{4}+16x^{2}+16\right)$$

Use the distributive property to multiply e by 4x^{4}+16x^{2}+16.

$$4ex^{4}+16ex^{2}+16e$$

Expand

$$4ex^{4}+16ex^{2}+16e$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x^{2}+4\right)^{2}.

$$e\left(4\left(x^{2}\right)^{2}+16x^{2}+16\right)$$

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

$$e\left(4x^{4}+16x^{2}+16\right)$$

Use the distributive property to multiply e by 4x^{4}+16x^{2}+16.

$$4ex^{4}+16ex^{2}+16e$$