Question

Fill in the blank to make the expression a perfect square.
v^2 + 8v +

Answer 1

`\large\boxed{v^2+8v+4^2=v^2+8v+16=(v+4)^2}`

Explanation:

Use

`(a+b)^2=a^2+2ab+b^2`

`v^2+8v=v^2+2(v)(4)\qquad\text{add}\ 4^2\ \text{to both sides}\\\\v^2+8v+4^2=v^2+2(v)(4)+4^2\\\\v^2+8v+16=v^2+2(v)(4)+4^2`