Question

Subtract: $\frac{7}{4} y^{3} + \frac{3}{5} y^{2} + \frac{1}{2} y + \frac{7}{2}$ from $\frac{9}{2} - \frac{y}{3} - \frac{y^{2}}{5}$

Accepted Answer

We have to subtract $\frac{7}{4} y^{3} + \frac{3}{5} y^{2} + \frac{1}{2} y + \frac{7}{2}$ from $\frac{9}{2} - \frac{y}{3} - \frac{y^{2}}{5}$ .

To subtract one algebraic expression from the other, first, we change the signs of all the terms of the expression which have to be subtracted and then add the two expressions.

Now, $(\frac{9}{2} - \frac{y}{3} - \frac{y^{2}}{5}) - (\frac{7}{4} y^{3} + \frac{3}{5} y^{2} + \frac{1}{2} y + \frac{7}{2})$

$= \frac{9}{2} - \frac{y}{3} - \frac{y^{2}}{5} - \frac{7}{4} y^{3} - \frac{3}{5} y^{2} - \frac{1}{2} y - \frac{7}{2}$

Grouping the like terms, we get,

$= (- \frac{7}{4} y^{3}) + (- \frac{y^{2}}{5} - \frac{3}{5} y^{2}) + (- \frac{y}{3} - \frac{1}{2} y) + (- \frac{7}{2} + \frac{9}{2})$

$= - \frac{7}{4} y^{3} + (- \frac{1}{5} - \frac{3}{5}) y^{2} + (- \frac{1}{3} - \frac{1}{2}) y + (\frac{- 7 + 9}{2})$

$= - \frac{7}{4} y^{3} + (\frac{- 1 - 3}{5}) y^{2} + (\frac{- 2 - 3}{6}) y + \frac{2}{2}$

$= - \frac{7}{4} y^{3} - \frac{4}{5} y^{2} - \frac{5}{6} y + 1$

Hence, the required difference is $- \frac{7}{4} y^{3} - \frac{4}{5} y^{2} - \frac{5}{6} y + 1$ .

Monicaa Abhijit Solutions for Chapter: Algebraic Expressions and Identities: Part I, Exercise 2: EXERCISE 5.2

Monicaa Abhijit Mathematics Solutions for Exercise - Monicaa Abhijit Solutions for Chapter: Algebraic Expressions and Identities: Part I, Exercise 2: EXERCISE 5.2

Questions from Monicaa Abhijit Solutions for Chapter: Algebraic Expressions and Identities: Part I, Exercise 2: EXERCISE 5.2 with Hints & Solutions

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