Question

Solve this :

Q. Using suitable identities factorise the following expressions.

$$\begin{gathered} 1.49y^2+84yz+36z^2 \\ 2.4x^2-8x+4 \\ 3.121b^2-88bc+16c^2 \end{gathered}$$

Answer 1

Dear student

$$\begin{gathered} 1)49{\mathrm{y}}^2+84\mathrm{yz}+36{\mathrm{z}}^2 \\ =(7\mathrm{y}{)}^2+2\left(7\mathrm{y}\right)\left(6\mathrm{z}\right)+(6\mathrm{z}{)}^2 \\ ={\left(7\mathrm{y}+6\mathrm{z}\right)}^2 \\ 2)4{\mathrm{x}}^2-8\mathrm{x}+4 \\ ={\left(2\mathrm{x}\right)}^2-2\left(2\mathrm{x}\right)\left(2\right)+2^2 \\ =(2\mathrm{x}-2{)}^2 \\ =4(\mathrm{x}-1{)}^2 \\ 3)121{\mathrm{b}}^2-88\mathrm{bc}+16{\mathrm{c}}^2 \\ =(11\mathrm{b}{)}^2-2\left(11\mathrm{b}\right)\left(4\mathrm{c}\right)+(4\mathrm{c}{)}^2 \\ ={\left(11\mathrm{b}-4\mathrm{c}\right)}^2 \\ \mathrm{Identities}\mathrm{used}: \\ {\left(\mathrm{a}\pm \mathrm{b}\right)}^2={\mathrm{a}}^2+{\mathrm{b}}^2\pm 2\mathrm{ab} \end{gathered}$$
Regards