Question

(Page 150)
Question
Addition and subraction of algebaric expressions
(i) m – n and m + n
(2) mn – 5 + 2n and nm + 2m – 3
(3) (xy/5) + (x/3) and (xy/2) – (x/3)

Answer 1

Addition and subtraction of algebraic expressions for the given expressions are given below respectively

(1) a) m-n+m+n=2m

    b) m-n-(m+n)=-2n

(2) a) mn-5+2n+nm+2m-3=2mn-8+2n+2m

    b) mn-5+2n-(nm+2m-3)=-2(1-n+m)

(3) a) $\frac{xy}{5}+\frac{x}{3}+\frac{xy}{2}-\frac{x}{3}=\frac{xy}{5}+\frac{xy}{2}$

    b) $\frac{xy}{5}+\frac{x}{3}-(\frac{xy}{2}-\frac{x}{3})=\frac{xy}{5}+2(\frac{x}{3})-\frac{xy}{2}$

Step-by-step explanation:

• Given algebraic expressions are

(1) m-n and m+n

(2) mn-5+2n and nm+2m-3

(3) $\frac{xy}{5}+\frac{x}{3}$ and $\frac{xy}{2}-\frac{x}{3}$

To find their algebraic addition and subtraction :

1) m-n and m+n

• Now do algebraic addition

m-n+m+n=2m

• Now do algebraic subtraction

m-n-(m+n)=m-n-m-n ( by distributive property )

=-2n

Therefore m-n-(m+n)=-2n

2) mn-5+2n and nm+2m-3

• Now do algebraic addition

mn-5+2n+nm+2m-3=mn-5+2n+mn+2m-3 ( by commutative property )

=2mn-8+2n+2m

Therefore mn-5+2n+nm+2m-3=2mn-8+2n+2m

• Now do algebraic subtraction

mn-5+2n-(nm+2m-3)=mn-5+2n-nm-2m+3  (by distributive property )

=-2+2n-2m

=-2(1-n+m)

Therefore mn-5+2n-(nm+2m-3)=-2(1-n+m)

3)  $\frac{xy}{5}+\frac{x}{3}$ and $\frac{xy}{2}-\frac{x}{3}$

• Now do algebraic addition

$\frac{xy}{5}+\frac{x}{3}+\frac{xy}{2}-\frac{x}{3}$

$=\frac{xy}{5}+\frac{xy}{2}$

Therefore $\frac{xy}{5}+\frac{x}{3}+\frac{xy}{2}-\frac{x}{3}=\frac{xy}{5}+\frac{xy}{2}$

• Now do algebraic subtraction

$\frac{xy}{5}+\frac{x}{3}-(\frac{xy}{2}-\frac{x}{3})$

$=\frac{xy}{5}+\frac{x}{3}-\frac{xy}{2}+\frac{x}{3}$

$=\frac{xy}{5}+2(\frac{x}{3})-\frac{xy}{2}$

Therefore $\frac{xy}{5}+\frac{x}{3}-(\frac{xy}{2}-\frac{x}{3})=\frac{xy}{5}+2(\frac{x}{3})-\frac{xy}{2}$