delsa20055 delsa20055
  • 04-02-2020
  • Mathematics
contestada

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

Respuesta :

renu21 renu21
  • 10-02-2020

'[tex](x+4)^2-1[/tex]' in the form of [tex](x+a)^2[/tex] - b.

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.

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