Error Analysis Your friend incorrectly factors the expression below as 7x(3 - 2xy). Factor the expression below correctly. What error did your friend make? 21x- 14xy Factor the expression. 21x - 14xy = (Factor completely.) %3D

Error Analysis Your friend incorrectly factors the expression below as 7x(3 - 2xy). Factor the expression below correctly. What error did your friend make? 21x- 14xy Factor the expression. 21x - 14xy = (Factor completely.) %3D

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter8: Polynomials

Section8.7: Factoring Special Products

Problem 3GP

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Question

Error Analysis Your friend incorrectly factors the expression below as 7x(3 - 2xy). Factor the
expression below correctly. What error did your friend make?
21x- 14xy
Factor the expression.
21x- 14xy = (Factor completely.)
%3D
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Expert Solution

Step 1 EXPLANATION

The given expression is

$21 x - 14 x y$

Now we factorize the given expression

$21 x - 14 x y$

$=$ $(3 \cdot 7 \cdot x - 2 \cdot 7 \cdot x \cdot y)$

$=$ $7 (3 \cdot x - 2 \cdot x \cdot y)$ ( factor out the common term $7$ )

$=$ $7 \cdot x (3 - 2 \cdot y)$ ( factor out the common term $x$ )

$= 7 x (3 - 2 y)$

$=$ $7 \times x \times (3 - 2 y)$

My friend make mistake in the term $(3 - 2 x y)$ because in the correct factorization it will be $(3 - 2 y)$

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