Solve (2x^2-5)^2+11

$$( 2 x ^ { 2 } - 5 ) ^ { 2 } + 11$$

Expand

$$4x^{4}-20x^{2}+36$$

Solution Steps

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

$$4\left(x^{2}\right)^{2}-20x^{2}+25+11$$

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

$$4x^{4}-20x^{2}+25+11$$

Add 25 and 11 to get 36.

$$4x^{4}-20x^{2}+36$$

Evaluate

$$\left(2x^{2}-5\right)^{2}+11$$

Solution Steps

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

$$4\left(x^{2}\right)^{2}-20x^{2}+25+11$$

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

$$4x^{4}-20x^{2}+25+11$$

Add 25 and 11 to get 36.

$$4x^{4}-20x^{2}+36$$