Math, asked by yugparekh50, 5 months ago

factories 27p³-1/216-9/2p²+1/4p​

Answers

Answered by Akankshapatel763
7

Answer:

your step by step answer is given in above attached pic.

Attachments:
Answered by Salmonpanna2022
20

Step-by-step explanation:

Given:-

 \tt{27 {p}^{3}  -  \frac{1}{216}  -  \frac{9}{2}  {p}^{2}  +  \frac{1}{4} p} \\  \\

What to do:-

To Factorise the expression.

Solution:-

Let's solve the problem,

We have,

 \tt{27 {p}^{3}  -  \frac{1}{216}  -  \frac{9}{2}  {p}^{2}  +  \frac{1}{4} p} \\  \\

⟹ \tt{(3p {)}^{2}  -  \bigg( \frac{1}{6}  \bigg )^{2}  -  \frac{3}{2} p \bigg(3p -  \frac{1}{6}  \bigg) }\\  \\

⟹  \tt{\bigg(3p -  \frac{1}{6 }\bigg)\left\{(3p {)}^{2} + 3p \times   \frac{1}{6}  +  \bigg({ \frac{1}{6} \bigg)^{2}  }\right\} -  \frac{3}{2} p \bigg(3p -  \frac{1}{6}  \bigg) }\\  \\ </p><p>

⟹  \tt{\bigg(3p -  \frac{1}{6}  \bigg) \bigg(9 {p}^{2}  + p \times  \frac{1}{2}  +  \frac{1}{36}  \bigg) -  \frac{3}{2} p \bigg(3p -  \frac{1}{6}  \bigg) }\\  \\

⟹  \tt{\bigg(3p -  \frac{1}{6}  \bigg) \bigg(9 {p}^{2}  +  \frac{p}{2}  +  \frac{1}{36}  -  \frac{3}{2} p \bigg)} \\  \\

⟹  \tt{\bigg(3p -  \frac{1}{6}  \bigg) \bigg(9 {p}^{2}  - p +  \frac{1}{36}  \bigg)} \\  \\

⟹  \tt{\bigg(3p -  \frac{1}{6}  \bigg) \left \{(3p {)}^{2} - 2 \times 3p \times  \frac{1}{6}   +  \bigg( \frac{1}{6}   \bigg)^{2} \right \} }\\  \\

⟹  \tt{\bigg(3p -  \frac{1}{6}  \bigg) \bigg(3p -  \frac{1}{6}  \bigg )^{2} } \\  \\

⟹  \tt{\bigg(3p -  \frac{1}{6}  \bigg) \bigg(3p -  \frac{1}{6}  \bigg) \bigg(3p -  \frac{1}{6}  \bigg) } \:  \:  \red{Ans}.\\  \\

I hope it's help you...☺

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