Ex.9.3 Q3 Algebraic Expressions and Identities - NCERT Maths Class 8

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Question

 Add the following.

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

(ii)\(\quad a\text{ }-\text{ }b\text{ }+\text{ }ab,\;b\text{ }-\text{ }c\text{ }+\text{ }bc\text{ },\;\text{ }c\text{ }-\text{ }a\text{ }+\text{ }ac\)

(iii)\(\quad 2{{p}^{2}}{{q}^{2}}-\text{ }3pq+\text{ }4,\;\text{ }5\text{ }+7pq\text{ }-3{{p}^{2}}{{q}^{2}}\)

(iv)\(\quad {l^2} + {m^2},\;{m^2} + {n^2},{n^2} + {l^2},\;2lm + 2mn + 2nl\)

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)

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

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

  
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