Solve [-(k+j)]^2+4(k-1)

$$[ - ( k + j ) ] ^ { 2 } + 4 ( k - 1 )$$

Evaluate

$$\left(j+k\right)^{2}+4k-4$$

Solution Steps

To find the opposite of k+j, find the opposite of each term.

$$\left(-k-j\right)^{2}+4\left(k-1\right)$$

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

$$k^{2}+2kj+j^{2}+4\left(k-1\right)$$

Use the distributive property to multiply 4 by k-1.

$$k^{2}+2kj+j^{2}+4k-4$$

Expand

$$j^{2}+2jk+k^{2}+4k-4$$

Solution Steps

To find the opposite of k+j, find the opposite of each term.

$$\left(-k-j\right)^{2}+4\left(k-1\right)$$

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

$$k^{2}+2kj+j^{2}+4\left(k-1\right)$$

Use the distributive property to multiply 4 by k-1.

$$k^{2}+2kj+j^{2}+4k-4$$