Step-by-step explanation:
We have,
[tex]x^2[/tex] + 8x + 15
To express [tex]x^2[/tex] + 8x + 15 in the form of [tex](x+a)^2[/tex] - b = ?
∴ [tex]x^2[/tex] + 8x + 15
Adding and subtracting 1, we get
= [tex]x^2[/tex] + 8x + 15 + 1 - 1
= [tex]x^2[/tex] + 8x + 16 - 1
= [tex]x^2[/tex] + 2(x)(4) + [tex]4^{2}[/tex] - 1
Using the algebraic identity,
[tex](x+y)^{2}=x^{2} +2xy+y^{2}[/tex]
= [tex](x+4)^2-1[/tex]
Thus, [tex](x+4)^2-1[/tex] in the form of [tex](x+a)^2[/tex] - b.
