Solve (x^2-5)^2-5(x^2-5)+4

$$( x ^ { 2 } - 5 ) ^ { 2 } - 5 ( x ^ { 2 } - 5 ) + 4$$

Evaluate

$$x^{4}-15x^{2}+54$$

Solution Steps

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

$$\left(x^{2}\right)^{2}-10x^{2}+25-5\left(x^{2}-5\right)+4$$

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

$$x^{4}-10x^{2}+25-5\left(x^{2}-5\right)+4$$

Use the distributive property to multiply -5 by x^{2}-5.

$$x^{4}-10x^{2}+25-5x^{2}+25+4$$

Combine -10x^{2} and -5x^{2} to get -15x^{2}.

$$x^{4}-15x^{2}+25+25+4$$

Add 25 and 25 to get 50.

$$x^{4}-15x^{2}+50+4$$

Add 50 and 4 to get 54.

$$x^{4}-15x^{2}+54$$

Expand

$$x^{4}-15x^{2}+54$$

Solution Steps

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

$$\left(x^{2}\right)^{2}-10x^{2}+25-5\left(x^{2}-5\right)+4$$

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

$$x^{4}-10x^{2}+25-5\left(x^{2}-5\right)+4$$

Use the distributive property to multiply -5 by x^{2}-5.

$$x^{4}-10x^{2}+25-5x^{2}+25+4$$

Combine -10x^{2} and -5x^{2} to get -15x^{2}.

$$x^{4}-15x^{2}+25+25+4$$

Add 25 and 25 to get 50.

$$x^{4}-15x^{2}+50+4$$

Add 50 and 4 to get 54.

$$x^{4}-15x^{2}+54$$