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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

4. Factoring Quadratic Expressions

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Exercise 78 Page 222

Try to think of the greatest common factor between the coefficients and between the variables separately.

GCF: xy
Expression: xy(xy+1)

Practice makes perfect

We want to find the greatest common factor (GCF) of the terms in the given expression. x^2y^2+xy To find the GCF of the variables, we need to identify the all possible variable factors in both terms. \begin{aligned} \textbf{Factors of }\bm{1^\textbf{st}}\textbf{ Variable:}&\ {\color{#0000FF}{x}}, x^2, {\color{#0000FF}{y}}, y^2, {\color{#FF0000}{xy}}, x^2y, xy^2, x^2y^2\\ \textbf{Factors of }\bm{2^\textbf{nd}}\textbf{ Variable:}&\ {\color{#0000FF}{x}}, {\color{#0000FF}{y}}, {\color{#FF0000}{xy}} \end{aligned} We see that there are two repeated variable factors. Their maximum exponents are x= x^1 and y= y^1. Therefore, the GCF of the variables is x* y= xy. Now we can write the given expression in terms of the GCF. x^2y^2+xy ⇔ xy* xy+ xy* 1 Finally, we will factor out the GCF. xy* xy+ xy*1 ⇔ xy(xy+1)

Checking Our Answer

Check your answer ✓

To check our answer, we can apply the Distributive Property and compare the result with the given expression.

xy(xy+1)

Distribute xy

xy(xy)+xy(1)

Multiply

x^2y^2+xy

After applying the Distributive Property, the result is the same as the given expression. Therefore, we can be sure our solution is correct!

Subchapter links

Lesson Check p.221

Practice and Problem-Solving Exercises p.221-223

Standardized Test Prep p.223

Mixed Review p.223