Question

Expand using formulae:

(1) (y – 3)²
(2) (4 + p)²
(3) (5 + m) (5 – m)
(4) ${\left(6+\frac{1}{n}\right)}^2$

Answer 1

(1) We know that (a – b)² = a² – 2ab + b²
Comparing (y – 3)² with (a – b)² , we get: a = y and b = 3,
Substituting these in the above formula:
(y – 3)² = y² – 2 × y × 3 + 3²
= y² – 6y + 9

(2) We know that (x + y)² = x² + 2xy + y² .
Comparing (4+ p)² with (x + y)² , we get: x = 4 and y = p
Substituting these in the above formula:
(4 + p)² = 16 + 2 × 4 × p + p²
= 16 + 8p + p²

(3) We know that $\left(a+b\right)\left(a-b\right)=a^2-b^2$ .
Comparing (5+m)(5-m) with (a+b)(a-b), we get:
a =5 and b = m
Substituting these in the above formula:

$$\begin{gathered} \left(5+m\right)\left(5-m\right)=5^2-m^2 \\ =25-m^2 \end{gathered}$$

(4) We know that (x + y)² = x² + 2xy + y² .
Comparing ${\left(6+\frac{1}{n}\right)}^2$ with (x + y)² , we get:
x = 6 and y = $\frac{1}{n}$
Substituting these in the above formula:

$$\begin{gathered} {\left(6+\frac{1}{n}\right)}^2=6^2+2\times 6\times \frac{1}{n}+{\left(\frac{1}{n}\right)}^2 \\ =36+\frac{12}{n}+\frac{1}{n^2} \end{gathered}$$