Identities - Finding Unlnown Coefficients

**GrigOrig99** · May 23rd 2012, 06:04 AM

Having a bit of trouble with this one. Can anyone help?

Many thanks.

Q. Find the values of a & b if $(2x+a)^2 = 4x^2+12x+b$ , for all x.

Attempt: $4x^2+4xa+a^2 = 4x^2+12x+b$
$4a = 12 => a = 3$
$a^2 = b => 3^2 = b => b = 9$

Ans. (From text book): a = 3, b = 7

**Plato** · May 23rd 2012, 06:39 AM

Originally Posted by GrigOrig99

Q. Find the values of a & b if $(2x+a)^2 = 4x^2+12x+b$ , for all x.

Attempt: $4x^2+4xa+a^2 = 4x^2+12x+b$
$4a = 12 => a = 3$
$a^2 = b => 3^2 = b => b = 9$

Ans. (From text book): a = 3, b = 7

The answer from the text is clearly wrong.
Say $x=1$ then $(2(1)+3)^2=25$ but $4(1)^2+12(1)+7=23.$

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