分解以下各项：
问题1. 6x(2x-y)+ 7y(2x-y)
解决方案：
As we know that (2x – y) is a common factor in the above expression.
So we will take out it and the expression can be written like,
(2x – y)(6x + 7y)
问题2。2r(y-x)+ s(x-y)
解决方案：
We know that
(y – x) = -(x – y) or (x – y) = -(y – x)
So we will write the above expression like
2r(y – x) – s(y – x)
Taking (y – x) as common from this expression
(2r – s)(y – x)
问题3. 7a(2x – 3)+ 3b(2x – 3)
解决方案：
We know that in this expression (2x – 3) is common factor,
So we take common from it.
(2x – 3)(7a + 3b)
问题4. 9a(6a – 5b)– 12a 2 (6a – 5b)
解决方案：
Taking (6a – 5b) common from the above expression
(9a – 12a2)(6a – 5b)
Now taking a common from it
9a – 12a2
=> 3 * 3a – 4 * 3a
=> 3a(3 – 4a)
Now writing 3a(3 – 4a) instead of (9a – 12a2)
3a(3 – 4a)(6a – 5b)
问题5. 5(x – 2y) 2 + 3(x – 2y)
解决方案：
Taking (x – 2y) common from the above expression
(x – 2y)[5(x – 2y) + 3]
=>(x – 2y)(5x – 10y + 3)
问题6. 16(2l – 3m) 2 – 12(3m – 2l)
解决方案：
Taking 2l – 3m = -(3m – 2l) or (3m – 2l) = -(2l – 3m)
So above expression can be written as
=> 16(2l – 3m)2 + 12(2l – 3m)
Taking common (2l – 3m)
=> (2l – 3m)[16(2l – 3m) + 12]
=> (2l – 3m){4[4(2l – 3m) + 3}
=> 4(2l – 3m)(8l – 12m + 3)
问题7. 3a(x – 2y)– b(x – 2y)
解决方案：
Taking (x – 2y) common from above expression
=> (x – 2y)(3a – b)
问题8. a 2 (x + y)+ b 2 (x + y)+ c 2 (x + y)
解决方案：
Taking (x + y) common from above expression
=>(x + y)[ a2 + b2 + c2]
问题9.(x – y) 2 +(x – y)
解决方案：
This can be written as
=>(x – y)(x – y) + (x – y)
Taking (x – y) common from the above expression
=> (x – y)[x – y + 1]
问题10. 6(a + 2b)– 4(a + 2b) 2
解决方案：
Taking (a + 2b) from the above expression
=> (a + 2b)[6 – 4(a + 2b)]
=> Again taking 2 as a common factor
=> 2(a + 2b)[3 – 2(a + 2b)]
=> 2(a + 2b)(3 – 2a – 4b)
问题11. a(x – y)+ 2b(y – x)+ c(x – y) 2
解决方案：
We can write
y – x = -(x – y)
then
=> a(x – y) – 2b(x – y) + c(x – y)2
Taking (x – y) from above expression
=> (x – y)(a – 2b + c(x – y))
=> (x – y)(a – 2b + cx – cy)
问题12. -4(x – 2y) 2 + 8(x – 2y)
解决方案：
Taking 4(x – 2y) as a common factor from expression
=> 4(x – 2y)[-(x – 2y) + 2]
=> 4(x – 2y)[2 – x + 2y]
问题13. x 3 (a – 2b)+ x 2 (a – 2b)
解决方案：
Taking x2(a – 2b) as common factor from above expression
=> x2(a – 2b)(x + 1)
问题14.(2x – 3y)(a + b)+(3x – 2y)(a + b)
解决方案：
Taking (a + b) as a common factor from expression
(a + b)(2x – 3y + 3x – 2y)
(a + b)(5x – 5y)
Taking 5 as common factor from (5x – 5y)
=> 5(a + b)(x – y)
问题15。4(x + y)(3a – b)+ 6(x + y)(2b – 3a)
解决方案：
Taking 2(x + y) as a common factor
=> 2(x + y)[2(3a – b) + 3(2b – 3a)]
=> 2(x + y)[6a – 2b + 6b – 9a]
=> 2(x + y)(4b – 3a)