Topic Content:
- Factorizing By Grouping
To factorize an expression containing four terms, you need to group the terms into pairs. Then factorize each pair of terms.
Worked Example 5.3.1:
Factorize the following by grouping:
a. \( \scriptsize x^2 + x \: – \: x \: – \:1\)
b. \( \scriptsize 6xy \: – \: 2x \: – \: 3y + 1\)
c. \( \scriptsize 6x^2 \: + \: 15x \: – \: 2x \: – \: 5 \)
d. \( \scriptsize 4a^3y \: – \: 4a^2bx \: + \: 2ay^2 \: – \: 2bxy \)
e. \( \scriptsize 6x^2 \: + \: 2xy \: – \: 6xy \: – \: 2y^2 \)
Solution
a. \( \scriptsize x^2 + x \: – \: x \: – \:1 \\ \scriptsize = (x^2 + x) \: – \: x \: – \:1 \\ \scriptsize(x^2 + x) \: – \: (x + 1) \\ \scriptsize x(x+1) \: – \: 1 (x + 1) \\ \scriptsize = (x \: – \:1)( x + 1)\)
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