How to factorise 4(x+y)(3a-2b)+(6x+y)(2b-3
a)
well, 2b-3a = -(3a-2b) so you have
4(x+y)(3a-2b)-(6x+y)(3a-2b)
...
y(3a-2b)-3a-2b
To factorize the given expression, we need to look for common factors within each term and then factor them out.
The given expression is: 4(x+y)(3a-2b) + (6x+y)(2b-3)
Step 1: Factor out common factors within each term:
In the first term (x+y) is common, and in the second term (2b-3) is common.
4(x+y)(3a-2b) + (6x+y)(2b-3)
= (x+y) * [4(3a-2b)] + (6x+y)(2b-3)
Step 2: Simplify each factor within the brackets:
4(3a-2b) simplifies to 12a - 8b
(6x+y)(2b-3) can be expanded using the distributive property:
= (6x+y)(2b) - (6x+y)(3)
= 12xb + 2by - 18x - 3y
Now we have:
(x+y)(12a-8b) + (12xb + 2by - 18x - 3y)
Step 3: Combine like terms:
In the first term, there are no like terms, so we can't simplify it further.
In the second term, we can combine like terms: 12xb - 18x gives us 6xb - 18x, and 2by - 3y can't be simplified any further.
Therefore, the fully factorized expression is:
(x+y)(12a-8b) + (6xb - 18x + 2by - 3y)