Question

If ${\mathrm{a}}^2+{\mathrm{b}}^2=\mathrm{z}$ and $\mathrm{ab}=\mathrm{y}$, what will be the equivalent of $4\mathrm{z}+8\mathrm{y}$?

Answer 1

Step- 1: Formula used:

By algebraic identity

${(\mathrm{a}+\mathrm{b})}^2={\mathrm{a}}^2+2\mathrm{ab}+{\mathrm{b}}^2$

Step- 2: Substituting the values:

Given that,

${\mathrm{a}}^2+{\mathrm{b}}^2=\mathrm{z}$

$\mathrm{ab}=\mathrm{y}$

Substituting the above values in given expression

$4\mathrm{z}+8\mathrm{y}=4({\mathrm{a}}^2+{\mathrm{b}}^2)+8\left(\mathrm{ab}\right)$

$4\mathrm{z}+8\mathrm{y}=4{\mathrm{a}}^2+4{\mathrm{b}}^2+8\mathrm{ab}$

$4\mathrm{z}+8\mathrm{y}=4({\mathrm{a}}^2+2\mathrm{ab}+{\mathrm{b}}^2)$

$4\mathrm{z}+8\mathrm{y}=4{(\mathrm{a}+\mathrm{b})}^2$

Therefore the value of $4\mathrm{z}+8\mathrm{y}$ is $4{(\mathrm{a}+\mathrm{b})}^2$.