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Math  /  Algebra

Questionlo, factorized completely 6ax=12by−9ay+8bx6 a x=12 b y-9 a y+8 b x

Studdy Solution

STEP 1

1. We are given an equation 6ax=12by−9ay+8bx6ax = 12by - 9ay + 8bx.
2. The goal is to factorize the equation completely.
3. Factorization involves expressing the equation as a product of its factors.

STEP 2

1. Rearrange the equation to bring all terms to one side.
2. Group terms with common factors.
3. Factor out the common factors.
4. Simplify the expression.

STEP 3

Rearrange the equation to bring all terms to one side:
6ax−12by+9ay−8bx=0 6ax - 12by + 9ay - 8bx = 0

STEP 4

Group terms with common factors. We can group the terms as follows:
(6ax−8bx)+(9ay−12by)=0 (6ax - 8bx) + (9ay - 12by) = 0

STEP 5

Factor out the common factors from each group:
From the first group 6ax−8bx6ax - 8bx, factor out 2x2x:
2x(3a−4b) 2x(3a - 4b)
From the second group 9ay−12by9ay - 12by, factor out 3y3y:
3y(3a−4b) 3y(3a - 4b)
Now the equation becomes:
2x(3a−4b)+3y(3a−4b)=0 2x(3a - 4b) + 3y(3a - 4b) = 0

STEP 6

Notice that (3a−4b) (3a - 4b) is a common factor in both terms. Factor out (3a−4b) (3a - 4b) :
(3a−4b)(2x+3y)=0 (3a - 4b)(2x + 3y) = 0
The completely factorized form of the equation is (3a−4b)(2x+3y)=0 \boxed{(3a - 4b)(2x + 3y) = 0} .

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