The following algebraic expression is given: xy + 5y + 2x + 10. What is the equivalent algebraic expression…

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The following algebraic expression is given: xy + 5y + 2x + 10. What is the equivalent algebraic expression when factored?

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here are the solutions for the remaining questions: ACTIVITY 2 The following algebraic expression is given: xy + 5y + 2x + 10 2.2 If we group the first two terms and the last two terms as follows: (xy + 5y) + (2x + 10) what do you notice about each group? In Group 1 (xy + 5y), the common factor is y. In Group 2 (2x + 10), the common factor is 2. 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: Write the equivalent algebraic expression. y(x + 5) + 2(x + 5) 2.4 What is the common factor in the two terms? The two terms are y(x + 5) and 2(x + 5). The common factor is (x + 5). 2.5 Use the distributive property to factor out this common factor and then express the polynomial as a product of two binomials. Step 1: Identify the common binomial factor, which is (x + 5). Step 2: Factor out (x + 5) from the expression y(x + 5) + 2(x + 5). (x + 5)(y + 2) 2.6 Joseph wants to factorize the following algebraic expression: 3x² + 6x + 4x + 8. Provide Joseph with a three-step guide on how to factorize the expression. Here's a three-step guide for Joseph: Step 1: Group the terms. Separate the expression into two pairs of terms: the first two terms and the last two terms. (3x² + 6x) + (4x + 8) Step 2: Factor out the greatest common factor (GCF) from each group. For the first group, 3x² + 6x, the GCF is 3x. Factoring it out gives 3x(x + 2). For the second group, 4x + 8, the GCF is 4. Factoring it out gives 4(x + 2). The expression becomes: 3x(x + 2) + 4(x + 2) Step 3: Factor out the common binomial. Notice that (x + 2) is a common factor in both terms. Factor it out to get the final factored form. (x + 2)(3x + 4)

The following algebraic expression is given: xy + 5y + 2x + 10. What is the equivalent algebraic expression when factored?

Answers

Step-by-step solution

Part 2.2

Part 2.3· 3 stepsy(x + 5) + 2(x + 5)

Factor out the common factor from Group 1.

Factor out the common factor from Group 2.

Write the equivalent algebraic expression.

Part 2.4(x + 5)

Part 2.5· 2 steps(x + 5)(y + 2)

Identify the common binomial factor, which is $(x + 5)$ .

Factor out $(x + 5)$ from the expression $y(x + 5) + 2(x + 5)$ .

Part 2.6· 3 steps(x + 2)(3x + 4)

Group the terms.* Separate the expression into two pairs of terms

Factor out the greatest common factor (GCF) from each group.

Factor out the common binomial.* Notice that $(x + 2)$ is a common factor in both terms.

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More Mathematics Questions

The following algebraic expression is given: xy + 5y + 2x + 10. What is the equivalent algebraic expression when factored?

Answers

Step-by-step solution

Part 2.2

Part 2.3· 3 stepsy(x + 5) + 2(x + 5)

Factor out the common factor from Group 1.

Factor out the common factor from Group 2.

Write the equivalent algebraic expression.

Part 2.4(x + 5)

Part 2.5· 2 steps(x + 5)(y + 2)

Identify the common binomial factor, which is (x+5)(x + 5)(x+5).

Factor out (x+5)(x + 5)(x+5) from the expression y(x+5)+2(x+5)y(x + 5) + 2(x + 5)y(x+5)+2(x+5).

Part 2.6· 3 steps(x + 2)(3x + 4)

Group the terms.* Separate the expression into two pairs of terms

Factor out the greatest common factor (GCF) from each group.

Factor out the common binomial.* Notice that (x+2)(x + 2)(x+2) is a common factor in both terms.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Identify the common binomial factor, which is $(x + 5)$ .

Factor out $(x + 5)$ from the expression $y(x + 5) + 2(x + 5)$ .

Factor out the common binomial.* Notice that $(x + 2)$ is a common factor in both terms.