Identities - Finding Unlnown Coefficients

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

Many thanks.

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

**Attempt:** $\displaystyle 4x^2+4xa+a^2 = 4x^2+12x+b$

$\displaystyle 4a = 12 => a = 3$

$\displaystyle a^2 = b => 3^2 = b => b = 9$

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

Re: Identities - Finding Unlnown Coefficients

Quote:

Originally Posted by

**GrigOrig99** **Q.** Find the values of a & b if $\displaystyle (2x+a)^2 = 4x^2+12x+b$, for all x.

**Attempt:** $\displaystyle 4x^2+4xa+a^2 = 4x^2+12x+b$

$\displaystyle 4a = 12 => a = 3$

$\displaystyle a^2 = b => 3^2 = b => b = 9$

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

The answer from the text is clearly wrong.

Say $\displaystyle x=1$ then $\displaystyle (2(1)+3)^2=25$ but $\displaystyle 4(1)^2+12(1)+7=23.$