Factorize fully 2.1 5ac+10ab-25ad
2.2 4x(a+b)-3y(a+b) 2.3 ax-bx+2a-2b 3.1 2(x+y) -t (x+y)
5ac+10ab-25ad = 5a(c+2b-5d)
4x(a+b)-3y(a+b) = (4x-3y)(a+b)
ax-bx+2a-2b = x(a-b)+2(a-b) = (x+2)(a-b)
2(x+y)-t(x+y) = (2-t)(x+y)
These are pretty straightforward. Look how they worked out, and try some more on your own. It just takes a little practice to get used to seeing the factors whioch can be pulled out.
To factorize the given expressions fully, we need to look for common factors and apply appropriate factoring techniques. Let's factorize each expression step by step:
2.1) 5ac + 10ab - 25ad
First, we can find the common factor, which is 5a. We can factor it out by dividing each term by 5a:
5ac + 10ab - 25ad = 5a(c + 2b - 5d)
So, the fully factorized expression is 5a(c + 2b - 5d).
2.2) 4x(a + b) - 3y(a + b)
Again, we can find the common factor, which is (a + b). We can factor it out by dividing each term by (a + b):
4x(a + b) - 3y(a + b) = (a + b)(4x - 3y)
So, the fully factorized expression is (a + b)(4x - 3y).
2.3) ax - bx + 2a - 2b
Here, we can factor common terms from the first two terms and the last two terms:
ax - bx + 2a - 2b = x(a - b) + 2(a - b)
Now we have a common factor, (a - b), that we can factor out:
x(a - b) + 2(a - b) = (a - b)(x + 2)
So, the fully factorized expression is (a - b)(x + 2).
3.1) 2(x + y) - t(x + y)
In this expression, (x + y) is a common factor that we can factor out:
2(x + y) - t(x + y) = (x + y)(2 - t)
So, the fully factorized expression is (x + y)(2 - t).
To factorize fully, identify any common factors and apply the factoring techniques accordingly.