**Exercise 6.2**

**1. Add the following algebraic expressions:**

** (i) **3**a**2**b****, −**4**a**2**b****, **9**a**2**b **

** ****Solution:**

To add the like terms, we proceed as follows:

3a^{2}b + (-4a^{2}b) + 9a^{2}b

= 3a^{2}b – 4a^{2}b + 9a^{2}b (Distributive Law)

= 8a^{2}b

**(iii) **4**xy**2**–**7**x**2**y****,**12**x**2**y****–**6**xy**2**, −**3**x**2**y****+**5**xy**2

**Solution:**

To add, we proceed as follows:

(4xy2–7x2y)+(12x2y)+(−6xy2)+(−3x2y+5xy2)

= 4xy2–7x2y+12x2y–6xy2–3x2y+5xy2

= 4xy2–6xy2+5xy2–7x2y+12x2y–3x2y (Collecting like terms)

= 3xy2+2x2y (Combining like terms)

**(iv) **32**a ****– **54**b****+**25**c****, **23**a****–**72**b****+**72**c****, **53**a****+**52**b****–**54**c**

** ****Solution:**

**(v) **112**xy****+**125**y****+**137**x****, −**112**y****–**125**x****–**137**xy**

**Solution:**

**(vi) **72**x**3**–**12**x**2**+**53**, **32**x**3**+**74**x**2**–****x****+**13 **,**32**x**2**–**52**x****–**2

**Solution:**

**2. Subtract:**

** (i) -5xy from 12xy**

**Solution: **

12xy – (–5xy)

= 12xy + 5xy = 17xy

**(ii) 2a ^{2} from -7a ^{2}**

**Solution: **

–7a^{2} – (2a^{2})

= –7a^{2} – 2a^{2 }= –9a^{2}

**(iii) 2a – b from 3a – 5b**

**Solution: **

(3a – 5b) – (2a – b)

= (3a – 5b) – 2a + b

= 3a – 5b – 2a + b

= 3a – 2a – 5b + b = a – 4b

**(iv) **2**x**^{3 }**– **4**x**^{2 }**+ **3**x ****+ **5 **from**4**x**^{3 }**+ ****x**^{2 }**+ ****x ****+ **6

**Solution: **

(4×3+x2+x+6)–(2×3–4×2+3x+5)

= 4×3+x2+x+6–2×3+4×2–3x–5

= 4×3–2×3+x2+4×2+x–3x+6–5 (Collecting like terms)

= 2×3+5×2–2x+1 (Combining like terms)

**3. Take away:**

**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.

**6. Subtract the sum 2x – x**^{2} + 5 and –4x – 3 + 7x^{2} from 5.

^{2}+ 5 and –4x – 3 + 7x

^{2}from 5.

**Solution:**

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

5 – {(2x – x^{2} + 5) + (–4x – 3 + 7x^{2})}

= 5 – (2x – 4x – x^{2} + 7x^{2} + 5 – 3)

= 5 – 2x + 4x + x^{2} – 7x^{2} – 5 + 3

= 5 – 5 + 3 – 2x + 4x + x^{2} – 7x^{2} (Collecting like terms)

= 3 + 2x – 6x^{2} (Combining like terms)

Thus, the answer is 3 + 2x – 6x^{2}.

**7. Simplify each of the following:**

** **** **

**(ii) [5-3x+2y-(2x-y)] – (3x-7y+9)**

**Solution:**

[5 – 3x +2y – (2x – y)] – (3x -7y + 9)

= [5 – 3x + 2y – 2x + y] –(3x – 7y + 9)

= [5- 5x + 3y ] – (3x – 7y + 9)

= 5 – 5x + 3y – 3x + 7y = -4 – 8x + 10y