Solve (5x-5)^2-(2x+1)^2+24

$$( 5 x - 5 ) ^ { 2 } - ( 2 x + 1 ) ^ { 2 } + 24$$

Evaluate

$$21x^{2}-54x+48$$

Solution Steps

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

$$25x^{2}-50x+25-\left(2x+1\right)^{2}+24$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+1\right)^{2}.

$$25x^{2}-50x+25-\left(4x^{2}+4x+1\right)+24$$

To find the opposite of 4x^{2}+4x+1, find the opposite of each term.

$$25x^{2}-50x+25-4x^{2}-4x-1+24$$

Combine 25x^{2} and -4x^{2} to get 21x^{2}.

$$21x^{2}-50x+25-4x-1+24$$

Combine -50x and -4x to get -54x.

$$21x^{2}-54x+25-1+24$$

Subtract 1 from 25 to get 24.

$$21x^{2}-54x+24+24$$

Add 24 and 24 to get 48.

$$21x^{2}-54x+48$$

Expand

$$21x^{2}-54x+48$$

Solution Steps

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

$$25x^{2}-50x+25-\left(2x+1\right)^{2}+24$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+1\right)^{2}.

$$25x^{2}-50x+25-\left(4x^{2}+4x+1\right)+24$$

To find the opposite of 4x^{2}+4x+1, find the opposite of each term.

$$25x^{2}-50x+25-4x^{2}-4x-1+24$$

Combine 25x^{2} and -4x^{2} to get 21x^{2}.

$$21x^{2}-50x+25-4x-1+24$$

Combine -50x and -4x to get -54x.

$$21x^{2}-54x+25-1+24$$

Subtract 1 from 25 to get 24.

$$21x^{2}-54x+24+24$$

Add 24 and 24 to get 48.

$$21x^{2}-54x+48$$