Question

Express x^2+8x+15 in the form (x+a)^2-b

Answer 1

'$(x+4)^2-1$' in the form of $(x+a)^2$ - b.

Step-by-step explanation:

We have,

$x^2$ + 8x + 15

To express $x^2$ + 8x + 15 in the form of  $(x+a)^2$ - b = ?

∴ $x^2$ + 8x + 15

Adding and subtracting 1, we get

= $x^2$ + 8x + 15 + 1 - 1

= $x^2$ + 8x + 16 - 1

= $x^2$ + 2(x)(4) + $4^{2}$ - 1

Using the algebraic identity,

$(x+y)^{2}=x^{2} +2xy+y^{2}$

= $(x+4)^2-1$

Thus, $(x+4)^2-1$ in the form of $(x+a)^2$ - b.