Question

Expand the following, using suitable identities: ${(\frac{1}{4}a-\frac{1}{2}b+1)}^2$ [3 MARKS]

Answer 1

Formula: 1 Mark
Substitution: 1 Mark
Calculation: 1 Mark

${(\frac{1}{4}a-\frac{1}{2}b+1)}^2$
Using the identity

${(a+b+c)}^2=a^2+b^2+c^2+2(ab+bc+ca)$ ....(1)

$a=\frac{1}{4}a,b=-\frac{1}{2}b,c=1$
Substituting the values of a,b,c in identity(1)

$={\left(\frac{1}{4}a\right)}^2+{(-\frac{1}{2}b)}^2+{\left(1\right)}^2+2\left(\frac{1}{4}a\right)(-\frac{1}{2}b)+2(-\frac{1}{2}b)\left(1\right)+2\left(1\right)\left(\frac{1}{4}a\right)$

$={\frac{1}{16}a}^2+{\frac{1}{4}b}^2+1-\frac{1}{4}ab-b+\frac{1}{2}a$