Chapter 6: Algebraic Expressions and Identities Exercise – 6.2

Question: 1

Add the following algebraic expressions:

Solution:

Question: 2

Subtract:

(i) – 5xy from 12xy

(ii) 2a² from -7a ²

(iii) 2a – b from 3a – 5b

Solution:

(i) 12xy – (–5xy)

= 12xy + 5xy = 17xy

(ii) –7a² – (2a²)

= –7a² – 2a² = –9a²

(iii) (3a – 5b) – (2a – b)

= (3a – 5b) – 2a + b

= 3a – 5b – 2a + b

= 3a – 2a – 5b + b = a – 4b

Question: 3

Take away:

Solution:

Question: 4

Subtract 3x – 4y – 7z from the sum of x – 3y + 2z and –4x + 9y – 11z

Solution:

First add the expressions x – 3y + 2z and –4x + 9y – 11z we get:

(x – 3y + 2z ) + (–4x + 9y – 11z)

= x – 3y + 2z – 4x + 9y – 11z

= x – 4x – 3y + 9y + 2z – 11z      (Collecting like terms)

= –3x + 6y – 9z         (Combining like terms)

Now, Subtracting the expression 3x – 4y – 7z from the above sum, we get:

(–3x + 6y – 9z) – (3x – 4y – 7z)

= – 3x + 6y – 9z – 3x + 4y + 7z

= – 3x – 3x + 6y + 4y – 9z + 7z       (Collecting like terms)

= – 6x + 10y – 2z          (Combining like terms)

Thus, the answer is – 6x + 10y – 2z.

Question: 5

Subtract the sum of 3l – 4m – 7n² and 2l + 3m – 4n² from the sum of 9l + 2m – 3n² and –3l + m + 4n².

Solution:

We have to subtract the sum of (3l – 4m – 7n²) and (2l + 3m – 4n²) from the sum of (9l + 2m – 3n²) and (–3l + m + 4n²)

{(9l + 2m – 3n²) + (–3l + m + 4n²)} – {(3l – 4m – 7n²) + (2l + 3m – 4n²)}

= (9l – 3l + 2m + m – 3n² + 4n²) – (3l + 2l – 4m + 3m – 7n² – 4n²)

= (6l + 3m + n²) – (5l – m – 11n²)       (Combining like terms inside the parenthesis)

= 6l + 3m + n² – 5l + m + 11n²

= 6l – 5l + 3m + m + n² + 11n²      (Collecting like terms)

= l + 4m + 12n²       (Combining like terms)

Thus, the required solution is l + 4m + 12n².

Question: 6

Subtract the sum 2x – x² + 5 and –4x – 3 + 7x² from 5.

Solution:

We have to subtract the sum of (2x – x² + 5) and (–4x – 3 + 7x²) from 5.

5 – {(2x – x² + 5) + (–4x – 3 + 7x²)}

= 5 – (2x – 4x – x² + 7x² + 5 – 3)

= 5 – 2x + 4x + x² – 7x² – 5 + 3

= 5 – 5 + 3 – 2x + 4x + x² – 7x²       (Collecting like terms)

= 3 + 2x – 6x²    (Combining like terms)

Thus, the answer is 3 + 2x – 6x².

Question: 7

Simplify each of the following:

Solution: