**Exercise 7.3**

**Factorize each of the following algebraic expressions:**

**1**. **6x (2x – y) + 7y(2x – y)**

**Solution:**

6x(2x – y) + 7y(2x – y)

= (6x + 7y)(2x – y) (taking (2x – y) as common factor)

**2**. **2r(y – x) + s(x – y)**

**Solution:**

2r(y – x) + s(x – y)

= 2r(y – x) – s(y – x) [since, (x – y) = -(y – x)]

= (2r –s)(y – x) [taking (y – x) as the common factor]

**3**. **7a(2x – 3) + 3b(2x – 3)**

**Solution:**

7a(2x – 3) + 3b(2x – 3)

= (7a + 3b)(2x – 3) [taking (2x – 3) as the common factor]

**4** .**9a(6a – 5b) – 12a**^{2}(6a – 5b)

^{2}(6a – 5b)

**Solution:**

9a(6a – 5b) – 12a^{2}(6a – 5b)

= (9a – 12qa^{2})(6a – 5b) [taking (6a – 5b) as the common factor]

= 3a(3 – 4a)(6a – 5b) [taking 3a as the common factor of the quadratic eqn. (9a – 12a^{2})]

**5**. **5(x – 2y)**^{2}+ 3(x – 2y)

^{2}+ 3(x – 2y)

**Solution:**

5(x – 2y)^{2} + 3(x – 2y)

= [(x – 2y) + 3](x – 2y) [taking (x – 2y) as the common factor]

= (5x – 10y + 3)(x – 2y)

**6. 16(2L – 3m)**^{2}-12(3m – 2L)

^{2}-12(3m – 2L)

**Solution:**

16(2L – 3m)^{2} – 12(3m – 2L)

= 16(2L – 3m)^{2} + 12(2L – 3m) [(3m – 2L) = -(2L – 3m)]

= [16(2L – 3m) + 12](2L – 3m) [taking (2L – 3m) as the common factor]

= 4[4(2L – 3m) + 3](2L – 3m) [taking 4 as the common factor (16(2L – 3m) + 12)]

= 4(8L – 12m + 3)(2L – 3m)

**7**. **3a(x – 2y) – b(x – 2y)**

**Solution:**

3a(x – 2y) – b(x – 2y)

= (3a -b)(x – 2y) [taking (x – 2y) as the common factor]

**8**. **a**^{2}(x + y) + b^{2}(x + y) + c^{2}(x + y)

^{2}(x + y) + b

^{2}(x + y) + c

^{2}(x + y)

**Solution:**

a^{2}(x + y) + b^{2}(x + y) +c^{2}(x + y)

= (a^{2} + b^{2} + c^{2})(x + y) [taking (x +y) as the common the factor]

**9** **. (x – y)**^{2} + (x – y)

^{2}+ (x – y)

**Solution:**

(x – y)^{2} + (x – y)

= (x – y)(x – y) + (x – y) [taking (x – y) as the common factor]

= (x – y + 1)(x – y)

**10**. **6(a + 2b) – 4(a +2b)**^{2}

^{2}

**Solution:**

6(a + 2b) – 4(a +2b)^{2}

= [6 – 4(a + 2b)](a + 2b) [taking (a + 2b as the common factor)]

= 2[3 – 2(a + 2b)](a + 2b) [taking 2 as the common factor of [6 – 4(a + 2b)]]

= 2(3 – 2a – 4b)(a + 2b)

**11**. **a(x – y) + 2b(y – x) + c(x – y)**^{2}

^{2}

**Solution:**

a(x – y) + 2b(y – x) + c(x – y)^{2}

= a(x – y) – 2b(x -y) +c(x – y)^{2} [(y -x) = -(x – y)]

= [a – 2b + c(x- y)](x – y)

= (a – 2b + cx – cy)(x- y)

**12**. **– 4(x – 2y)**^{2}+ 8(x – 2y)

^{2}+ 8(x – 2y)

**Solution:**

-4(x – 2y)^{2} + 8(x – 2y)

= [-4(x – 2y) + 8](x -2y) [taking (x – 2y) as the common factor]

= 4[-(x – 2y) + 2](x – 2y) [taking 4 as the common factor of [-4(x – 2y) + 8]]

= 4(2y – x + 2)(x – 2y)

**13**. **x**^{3}(a – 2b) + x^{2}(a – 2b)

^{3}(a – 2b) + x

^{2}(a – 2b)

**Solution:**

x^{3}(a – 2b) + x^{2}(a – 2b)

= (x^{3} + x^{2})(a – 2b) [taking (a – 2b) as the common factor]

= x^{2}(x + 1)(a – 2b) [taking x^{2} as the common factor of (x^{3} + x^{2})]

**14. (2x – 3y)(a + b) + (3x – 2y)(a + b)**

**Solution:**

(2x – 3y)(a + b) + (3x – 2y)(a + b)

= (2x – 3y + 3x – 2y)(a +b) [taking (a +b) as the common factor]

= (5x – 5y)(a + b)

= 5(x – y)(a + b) [taking 5 as the common factor of (5x – 5y)]

**15. 4(x + y)(3a – b) + 6(x + y)(2b – 3a)**

**Solution:**

4(x + y)(3a – b) + 6(x + y)(2b – 3a)

= 2(x + y)[2(3a – b) + 3(2b – 3a)] [taking (2(x + y)) as the common factor]

= 2(x + y)(6a – 2b + 6b – 9a)

= 2(x + y)(4b – 3a)