Solve (x^2-44)^2+10(44-x^2)+25

$$( x ^ { 2 } - 44 ) ^ { 2 } + 10 ( 44 - x ^ { 2 } ) + 25$$

Evaluate

$$\left(x^{2}-49\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{2}-44\right)^{2}.

$$\left(x^{2}\right)^{2}-88x^{2}+1936+10\left(44-x^{2}\right)+25$$

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

$$x^{4}-88x^{2}+1936+10\left(44-x^{2}\right)+25$$

Use the distributive property to multiply 10 by 44-x^{2}.

$$x^{4}-88x^{2}+1936+440-10x^{2}+25$$

Add 1936 and 440 to get 2376.

$$x^{4}-88x^{2}+2376-10x^{2}+25$$

Combine -88x^{2} and -10x^{2} to get -98x^{2}.

$$x^{4}-98x^{2}+2376+25$$

Add 2376 and 25 to get 2401.

$$x^{4}-98x^{2}+2401$$

Expand

$$x^{4}-98x^{2}+2401$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{2}-44\right)^{2}.

$$\left(x^{2}\right)^{2}-88x^{2}+1936+10\left(44-x^{2}\right)+25$$

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

$$x^{4}-88x^{2}+1936+10\left(44-x^{2}\right)+25$$

Use the distributive property to multiply 10 by 44-x^{2}.

$$x^{4}-88x^{2}+1936+440-10x^{2}+25$$

Add 1936 and 440 to get 2376.

$$x^{4}-88x^{2}+2376-10x^{2}+25$$

Combine -88x^{2} and -10x^{2} to get -98x^{2}.

$$x^{4}-98x^{2}+2376+25$$

Add 2376 and 25 to get 2401.

$$x^{4}-98x^{2}+2401$$