Question

Solve this :

Q. Using suitable identities factorise the following expressions.

​$$\begin{gathered} 1.a^2+8a+16 \\ 2.p^2-10p+25 \\ 3.25m^2+30m+9 \end{gathered}$$

Answer 1

Dear student
$$\begin{gathered} 1){\mathrm{a}}^2+8\mathrm{a}+16 \\ ={\mathrm{a}}^2+4\mathrm{a}+4\mathrm{a}+16 \\ =\mathrm{a}\left(\mathrm{a}+4\right)+\mathrm{a}(\mathrm{a}+4) \\ =\left(\mathrm{a}+4\right)\left(\mathrm{a}+4\right) \\ =(\mathrm{a}+4{)}^2 \\ 2){\mathrm{p}}^2-10\mathrm{p}+25 \\ ={\mathrm{p}}^2-5\mathrm{p}-5\mathrm{p}+25 \\ =\mathrm{p}\left(\mathrm{p}-5\right)-5\left(\mathrm{p}-5\right) \\ =\left(\mathrm{p}-5\right)\left(\mathrm{p}-5\right) \\ =(\mathrm{p}-5{)}^2 \end{gathered}$$
Similarly try other parts,
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