RS Aggarwal solution class 8 chapter 6 Operations on Algebraic Expressions Exercise 6A

Exercise 6A

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Q1 | Ex-6A | Class 8 | RS AGGARWAL | chapter 6 |Operations on Algebraic Expressions | myhelper

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Question 1:

Add:
8ab, −5ab, 3ab, −ab

Answer 1:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:


________
   $5ab$
​

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Question 2:

Add:
7x, −3x, 5x, −x, −2x

Answer 2:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:


_____
$6x$

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Question 3:

Add:
3a − 4b + 4c, 2a + 3b − 8c, a − 6b + c

Answer 3:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:


___________

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Question 4:

Add:
5x − 8y + 2z, 3z − 4y − 2x, 6y − z − x and 3x − 2z − 3y

Answer 4:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:

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Question 5:

Add:
6ax − 2by + 3cz, 6by − 11ax − cz and 10cz − 2ax − 3by

Answer 5:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:

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Question 6:

Add:
2x³ − 9x² + 8, 3x² − 6x − 5, 7x³ − 10x + 1 and 3 + 2x − 5x² − 4x³

Answer 6:

On arranging the terms of the given expressions in the descending powers of $x$ and adding column-wise:

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Question 7:

Add:
6p + 4q − r + 3, 2r − 5p − 6, 11q − 7p + 2r − 1 and 2q − 3r + 4

Answer 7:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise:

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Question 8:

Add:
4x² − 7xy + 4y² − 3, 5 + 6y² − 8xy + x² and 6 − 2xy + 2x² − 5y²

Answer 8:

On arranging the terms of the given expressions in the descending powers of $x$ and adding column-wise:

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Question 9:

Subtract:
3a²b from −5a²b

Answer 9:

On arranging the terms of the given expressions in the descending powers of $x$ and subtracting:

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Question 10:

Subtract:
−8pq from 6pq

Answer 10:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:

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Question 11:

Subtract:
−2abc from −8abc

Answer 11:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:

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Question 12:

Subtract:
−16p from −11p

Answer 12:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:

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Question 13:

Subtract:
2a − 5b + 2c − 9 from 3a − 4b − c + 6

Answer 13:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:

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Question 14:

Subtract:
−6p + q + 3r + 8 from p − 2q − 5r − 8

Answer 14:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:

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Question 15:

Subtract:
x³ + 3x² − 5x + 4 from 3x³ − x² + 2x − 4

Answer 15:

On arranging the terms of the given expressions in the descending powers of $x$ and subtracting column-wise:

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Question 16:

Subtract:
5y⁴ − 3y³ + 2y² + y − 1 from 4y⁴ − 2y³ − 6y² − y + 5

Answer 16:

Arranging the terms of the given expressions in the descending powers of $x$ and subtracting column-wise:

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Question 17:

Subtract:
4p² + 5q² − 6r² + 7 from 3p² − 4q² − 5r² − 6

Answer 17:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:

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Question 18:

What must be subtracted from 3a² − 6ab − 3b² − 1 to get 4a² − 7ab − 4b² + 1?

Answer 18:

Let the required number be $x$.





∴ Required number = $-a^2+ab+b^2-2$

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Question 19:

The two adjacent sides of a rectangle are 5x² − 3y² and x² + 2xy. Find the perimeter.

Answer 19:

Sides of the rectangle are $l$ and $b$.
$$\begin{gathered} l=5x^2-3y^2 \\ b=x^2+2xy \end{gathered}$$
Perimeter of the rectangle is $(2l+2b)$.

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Question 20:

The perimeter of a triangle is 6p² − 4p + 9 and two of its sides are p² − 2p + 1 and 3p² − 5p + 3. Find the third side of the triangle.

Answer 20:

Let $a, b and c$ be the three sides of the triangle.

∴ Perimeter of the triangle =$(a+b+c)$

Given perimeter of the triangle = $6p^2-4p+9$
One side ($a$)  = $p^2-2p+1$
Other side ($b$) = $3p^2-5p+3$
Perimeter = $(a+b+c)$


Thus, the third side is .