Question

2. Solve 5 examples for each identity that you use for factorization
i)a2+b2 +2ab= (a+b)2
ii)a2+b2-2ab=(a-b)2
iii)a3+b3 = (a+b)(a2+b2-ab)

Answer 1

Dear student
$$\begin{gathered} Takea=5andb=2\left(say\right) \\ 1){\left(a+b\right)}^2=a^2+b^2+2ab \\ \Rightarrow {\left(5+2\right)}^2=5^2+2^2+2\left(5\right)\left(2\right) \\ \Rightarrow 7^2=25+4+20 \\ \Rightarrow 49=49 \\ 2){\left(a-b\right)}^2=a^2+b^2-2ab \\ \Rightarrow {\left(5-2\right)}^2=5^2+2^2-2\left(5\right)\left(2\right) \\ \Rightarrow 3^2=25+4-20 \\ \Rightarrow 9=9 \\ 3)a^3+b^3=\left(a+b\right)\left(a^2+b^2-ab\right) \\ \Rightarrow 5^3+2^3=\left(5+2\right)\left(5^2+2^2-\left(5\right)\left(2\right)\right) \\ \Rightarrow 125+8=7\times 19 \\ \Rightarrow 133=133 \\ Similarlyyoucantakedifferentvaluesandprovetheidentities. \\ Regards \end{gathered}$$