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Question
Factorize each of the following expressions:
x2 + xy + xz + yz
Sum
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Solution
\[x^2 + xy + xz + yz\]
\[ = ( x^2 + xy) + (xz + yz)\] [Grouping the expressions]
\[ = x(x + y) + z(x + y)\]
\[ = (x + z)(x + y)\] [Taking (x + y) as the common factor]
\[ = (x + y)(x + z)\]
\[ = ( x^2 + xy) + (xz + yz)\] [Grouping the expressions]
\[ = x(x + y) + z(x + y)\]
\[ = (x + z)(x + y)\] [Taking (x + y) as the common factor]
\[ = (x + y)(x + z)\]
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