x² - 49 + 2x + 1
= (x² + 2x + 1) - 49
= (x + 1)² - 7²
= (x + 1 - 7)(x + 1 + 7)
= (x - 6)(x + 8)
\(x^2-49+2x+1=\left(x^2-2x+1\right)-49=\left(x-1\right)^2-7^2=\left[\left(x-1\right)-7\right]\left[\left(x-1\right)+7\right]=\left(x-1-7\right)\left(x-1+7\right)=\left(x-8\right)\left(x+6\right)\)
`x^2 - 49 + 2x+1`
`=(x^2+2x+1)-49`
`=(x+1)^2 - 7^2`
`=(x+1-7)(x+1+7)`
`=(x-6)(x+8)`