question_answer

Factorise:

(a) \[12x+36\]

(b) \[22y-33z\]

Answer:

(a) We have,       \[12x=\text{ }3\times 2\times 2\times x~\]

\[=\left( 2\times 2\times 3 \right)\times \text{ }x\]

\[36=2\times 2\times 3\times 3\]

\[=\left( 2\times 2\times 3 \right)\times 3~\]

\[\therefore \]\[12x+36=\left[ \left( 2\times 2\times 3 \right)\times \text{ }x \right]+\left[ \left( 2\times 2\times 3 \right)\times 3 \right]\]

\[=\text{ }2\times 2\times 3\left[ x+3 \right]\]

\[=\text{ }12\left( x+3 \right)~\]

(b) We have           \[22y=\text{ }2\times 11\times y\]

\[332=3\times 11\times 2\]

\[22y+33z=2\times 11\times y+3\times 11\times 2\]

\[=11\left( 2y+3z \right)\]