Gujarat BoardEnglish MediumSTD 8MATHSFactorization1 Mark
MCQ
Factorize $12ab(9a^2 - 16b^2) \div 3ab(3a + 3b)$
A
$(3a - 4b)$
B
$(3a + 3b)$
C
$(3a + 4b)$
✓
$(3a - 4b)$
✓
Answer
Correct option: D.
$(3a - 4b)$
D. $(3a - 4b)$ Solution:
Express the division as a fraction
$\frac{12\text{ab}(9\text{a}^2-16\text{b}^2)}{3\text{ab}(3\text{a}+4\text{b})}$
$\Rightarrow\frac{12\text{ab}((3\text{a})^3-(4\text{b}^2))}{3\text{ab}(3\text{a}+4\text{b})}$
$\Rightarrow\frac{12\text{ab}(3\text{a}+4\text{b})(3\text{a}-4\text{b})}{3\text{ab}(3\text{a}+4\text{b})}$
$\Rightarrow\frac{3\times4\text{ab}(3\text{a}+4\text{b})(3\text{a}-4\text{b})}{3\text{ab}(3\text{a}+4\text{b})}$
Cancel the common factors in the numerator and denominator
$\Rightarrow4(3\text{a}-4\text{b})$
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