Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 173226 by AgniMath last updated on 08/Jul/22

    Factorize the following equation:     (1/4) (a + b)^2  − (9/(16)) (2a − b)^2

$$\:\:\:\:\boldsymbol{\mathrm{Factorize}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\:\:\frac{\mathrm{1}}{\mathrm{4}}\:\left({a}\:+\:{b}\right)^{\mathrm{2}} \:−\:\frac{\mathrm{9}}{\mathrm{16}}\:\left(\mathrm{2}{a}\:−\:{b}\right)^{\mathrm{2}} \\ $$

Commented by mr W last updated on 08/Jul/22

=(((a+b)/2))^2 −[((3(2a−b))/4)]^2   =(((a+b)/2)+((3(2a−b))/4))(((a+b)/2)−((3(2a−b))/4))  =(((8a−b)(5b−4a))/(16))

$$=\left(\frac{{a}+{b}}{\mathrm{2}}\right)^{\mathrm{2}} −\left[\frac{\mathrm{3}\left(\mathrm{2}{a}−{b}\right)}{\mathrm{4}}\right]^{\mathrm{2}} \\ $$$$=\left(\frac{{a}+{b}}{\mathrm{2}}+\frac{\mathrm{3}\left(\mathrm{2}{a}−{b}\right)}{\mathrm{4}}\right)\left(\frac{{a}+{b}}{\mathrm{2}}−\frac{\mathrm{3}\left(\mathrm{2}{a}−{b}\right)}{\mathrm{4}}\right) \\ $$$$=\frac{\left(\mathrm{8}{a}−{b}\right)\left(\mathrm{5}{b}−\mathrm{4}{a}\right)}{\mathrm{16}} \\ $$

Commented by peter frank last updated on 08/Jul/22

thanks

$$\mathrm{thanks} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com