question_answer

Carry out the following divisions :

(a) \[28{{x}^{4}}\div 56x\]

(b) \[-36{{y}^{3}}\div 9{{y}^{2}}\]

(c) \[66p{{q}^{2}}{{r}^{3}}\div 11q{{r}^{2}}\]

(d)\[34{{x}^{3}}{{y}^{3}}{{z}^{3}}\div 51x{{y}^{3}}{{z}^{3}}\]

Answer:

(a) \[28{{x}^{4}}\div \text{ }56x=\frac{28{{x}^{4}}}{56x}\]

\[=\frac{2\times 2\times 7\times x\times x\times x\times x}{2\times 2\times 2\times 7\times x}\]

\[=\frac{{{x}^{3}}}{2}\]

(b) \[\text{ }36{{y}^{3}}\div \text{ }9{{y}^{2}}=\frac{-36{{y}^{3}}}{9{{y}^{2}}}\]

\[=\frac{-2\times 2\times 3\times 3\times y\times y\times y}{3\times 3\times y\times y}\]

\[=-4y\]

(c) \[66p{{q}^{2}}{{r}^{3}}\div \text{ }11q{{r}^{2}}=\frac{66p{{q}^{2}}{{r}^{3}}}{11q{{r}^{2}}}\]

\[=\frac{6\times 11\times p\times q\times q\times r\times r\times r}{11\times q\times r\times r}\]

= 6pqr

(d) \[34{{x}^{3}}{{y}^{3}}{{z}^{3}}\div \text{ }51x{{y}^{2}}{{z}^{3}}\]

\[=\frac{2\times 17\times x\times x\times y\times y\times y\times z\times z\times z}{3\times 17\times x\times y\times y\times z\times z\times z}\]

\[=\frac{2{{x}^{2}}y}{3}\]