# Ex.9.1 Q3 Algebraic Expressions and Identities - NCERT Maths Class 8

## Question

Add the following.

(i)\(\quad ab\text{ }-\text{ }bc,\; bc\text{ }-\text{ }ca,\; ca\text{ }-\text{ }ab\)

(ii)\(\begin{align} \begin{Bmatrix} a - b + ab,\\ b- c + bc ,\\ c - a + ac \end{Bmatrix} \end{align}\)

(iii)\(\begin{align} \begin{Bmatrix} \quad 2{{p}^{2}}{{q}^{2}}-3pq+4,\\ 5+7pq -3{{p}^{2}}{{q}^{2}} \end{Bmatrix} \end{align}\)

(iv)\(\begin{align} \begin{Bmatrix} {l^2} + {m^2},\\ {m^2} + {n^2},{n^2} + {l^2},\\ 2lm + 2mn + 2nl \end{Bmatrix} \end{align}\)

## Text Solution

**What is known?**

Expressions

**What is unknown?**

Addition

**Reasoning:**

Addition will take place between like terms.

**Steps:**

The given expressions written in separate rows, with like terms one below the other

and then the addition of these expressions are as follows.

(i)

\[\frac{\begin{align}\,\,&\,\,\,\,\,ab - bc\\&+\qquad bc - ca\\&+ \, - ab\; + ca\end{align}}{0}\]

Thus, the sum of the given expressions is \(0.\)

(ii)

\[\frac{\begin{align} & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,a-b+ab \\& +\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,b\,\,\,\,\,\,\,\,\,\,\,\,\,\,-c+bc \\& +\,\,\,\,\,\,\,\,-a\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+c\,\,\,\,\,\,\,\,\,\,\,\,+ac \\\end{align}}{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,ab+\,\,\,\,\,\,\,\,bc\,\,\,\,\,\,\,\,+ac}\]

Thus, the sum of the given expressions is \(ab + bc + ac.\)

(iii)

\[\frac{\begin{align}2{p^2}{q^2} \;-\; 3pq\; + \;4\\+ \,\,\, - 3{p^2}{q^2}\;+\; 7pq \;+\; 5\end{align}}{{\,\,\,\,\,\, - {p^2}{q^2}\;\; + \;\;4pq\;\; +\;\; 9}}\]

Thus, the sum of the given expressions is \( - {p^2}{q^2} + 4pq + 9.\)

(iv)

\[\frac{\begin{align}& \,\,\,\,\,\,{{l}^{2}}+{{m}^{2}} \\& +\,\,\,\,+{{m}^{2}}+{{n}^{2}} \\& +{{l}^{2}}\qquad \; \;+{{n}^{2}} \\& + \qquad \qquad \quad \; 2lm+2mn+2nl \\\end{align}}{\begin{align} 2{{l}^{2}}& +2{{m}^{2}} +2{{n}^{2}} \\ &+2lm+2mn+2nl \end{align}}\]

Thus, the sum of the given expressions is \(2\)(\({{l}^{2}}+{{m}^{2}}+{{n}^{2}}+lm+mn+nl\))