Equivalent Expressions Question 1

If $(x-1)^2=x^2-6x+b$ , where $a$ and $b$ are constants, what is the value of $b$ ?

-6

-3

3

9

Approach

Expand the equation on the left side and compare it with the equation on the right side:

(x-a)^2 = x^2-6x+b

x^2-2ax+a^2=x^2-6x+b

x^2 \colorbox{yellow}{\(-2ax\)} + \colorbox{aqua}{\(a^2\)}= x^2 \colorbox{yellow}{\(-6x\)}+\colorbox{aqua}{\(b\)}

Comparing corresponding parts,

Linear terms

-2ax=-6x

a=3

Constant terms

a^2=b

3^2=b

\boxed{9}=b