Math  /  Algebra

QuestionFactor xy+4y5x20x y+4 y-5 x-20
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Studdy Solution

STEP 1

1. The expression xy+4y5x20 xy + 4y - 5x - 20 is a polynomial that can be factored by grouping.
2. We will look for common factors in pairs of terms to simplify the expression.

STEP 2

1. Group the terms in pairs to find common factors.
2. Factor out the common factors from each group.
3. Identify and factor out the common binomial factor.

STEP 3

Group the terms in pairs:
(xy+4y)+(5x20) (xy + 4y) + (-5x - 20)

STEP 4

Factor out the common factor from each group:
From the first group (xy+4y) (xy + 4y) , factor out y y :
y(x+4) y(x + 4)
From the second group (5x20) (-5x - 20) , factor out 5-5:
5(x+4) -5(x + 4)
Now the expression is:
y(x+4)5(x+4) y(x + 4) - 5(x + 4)

STEP 5

Notice that (x+4) (x + 4) is a common factor in both terms. Factor out (x+4) (x + 4) :
(x+4)(y5) (x + 4)(y - 5)
The factored form of the expression is:
(x+4)(y5) \boxed{(x + 4)(y - 5)}

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