How can we factor the expression xy + 5y + 2x + 10 by grouping?

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2.1 What do you notice about all 4 terms? The four terms xy, 5y, 2x, and 10 do not have a common factor other than 1. 2.2 If we group the first two terms and the last two terms as follows: Group 1 (xy + 5y) + Group 2 (2x + 10). What do you notice about each group? In Group 1 (xy + 5y), y is a common factor. In Group 2 (2x + 10), 2 is a common factor. After factoring out the common factor from each group, the remaining binomial factor will be the same. 2.3 Factor these values out of each group and then write down the equivalent algebraic expression. Step 1: Factor out the common factor from Group 1. xy + 5y = y(x + 5) Step 2: Factor out the common factor from Group 2. 2x + 10 = 2(x + 5) Step 3: Substitute the factored groups back into the expression. y(x + 5) + 2(x + 5) Step 4: Factor out the common binomial factor (x + 5). (x + 5)(y + 2) The equivalent algebraic expression is (x + 5)(y + 2).

How can we factor the expression xy + 5y + 2x + 10 by grouping?

Answer

Step-by-step solution

Part 2.1

Part 2.2

Part 2.3· 4 steps(x + 5)(y + 2)

Factor out the common factor from Group 1.

Factor out the common factor from Group 2.

Substitute the factored groups back into the expression.

Factor out the common binomial factor $(x + 5)$ .

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How can we factor the expression xy + 5y + 2x + 10 by grouping?

Answer

Step-by-step solution

Part 2.1

Part 2.2

Part 2.3· 4 steps(x + 5)(y + 2)

Factor out the common factor from Group 1.

Factor out the common factor from Group 2.

Substitute the factored groups back into the expression.

Factor out the common binomial factor (x+5)(x + 5)(x+5).

Try one yourself

Still stuck on this one?

More Mathematics Questions

Factor out the common binomial factor $(x + 5)$ .