Question

Use factoring by grouping to factorize the following

1). 4au+24av−5bu−30bv solve for this

2). 15xw+18xk+25yw+30yk solve for this too

3). 10xy+30+25x+12y and this thank u

Answer 1

Step-by-step explanation:

kindly see the images for solution

Answer 2

The answers are  Q1) (u + 6v)(4a - 5b)           Q2) (5w + 6k)(3x + 5y)       Q3) (2y + 5)(5x + 6)

Given

1. 4au+24av−5bu−30bv solve for this
2. 15xw+18xk+25yw+30yk
3. 10xy+30+25x+12y

To Find

Factors by Grouping

Solution

For the grouping method-

• We consider groups of two terms together and factorize them according to their common terms.
• Then the common factor among the groups is taken commonly to give us the final answer

Q1)

4au+24av−5bu−30bv

Taking 4au+24av as one group and −5bu−30bv as another we write

(4au+24av) + (−5bu−30bv)

Taking 4a common from group 1 and -5b from group 2 we get

4a(u + 6v) -5b(u+6v)

Now, taking (u + 6v) common we get,

(u + 6v)(4a - 5b)

Hence (u + 6v)(4a - 5b) is the answer

Q2)

Using the steps as before we get

15xw+18xk+25yw+30yk

= (15xw+18xk) + (25yw+30yk)

= 3x(5w + 6k) + 5y(5w + 6k)

= (5w + 6k)(3x + 5y)

Hence, (5w + 6k)(3x + 5y) is the answer.

Q3)

Here we first need to arrange the expression in such a way that we can get a common term.

Hence we will interchange the position of 30 and 25x

Therefore, 10xy + 30 + 25x + 12y

= 10xy + 25x +30 +12y

Now we will repeat the same procedure we did in the previous question

10xy + 25x +30 +12y

= (10xy + 25x) +(30 +12y)

=5x(2y + 5) + 6(5 + 2y)

=(2y + 5)(5x + 6)

Hence (2y + 5)(5x + 6) is the answer.

Hence the answers are:-

Q1) (u + 6v)(4a - 5b)

Q2) (5w + 6k)(3x + 5y)

Q3) (2y + 5)(5x + 6)

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