chezmarylou1i

2021-12-21

Find the value of the given expressions
a) ${\left(2+3\right)}^{2};$
${2}^{2}+{3}^{2}$
b) ${\left(8+10\right)}^{2};$
${8}^{2}+{10}^{2}$
c) Check whether the given statement is true or false:
$Thegiven\mathrm{exp}ressionsarePSK{\left(a+b\right)}^{2}={a}^{2}+{b}^{2}$

Timothy Wolff

Expert

Step 1
a) Given: ${\left(2+3\right)}^{2};$
${2}^{2}+{3}^{2}$
USe algebraic identity
${\left(x+y\right)}^{2}={x}^{2}+2xy+{y}^{2}$
${\left(2+3\right)}^{2}$
$={2}^{2}+2×2×3+{3}^{2}$
$=4+12+9$
$=25$
Step 2
And ${2}^{2}+{3}^{2}$
$=4+9$
$=13$
Hence thevalue of the expression ${\left(2+3\right)}^{2}$ is 25 and ${2}^{2}+{3}^{2}$ is 13

Mary Goodson

Expert

Step 1
b) Given:
${\left(8+10\right)}^{2}$
${8}^{2}+{10}^{2}$
Use algebraic identity
${\left(x+y\right)}^{2}={x}^{2}+2xy+{y}^{2}$
${\left(8+10\right)}^{2}$
$={8}^{2}+2×8×10+{10}^{2}$
$=64+160+100$
$=342$
Step 2
And
${8}^{2}+{10}^{2}$
$=64+100$
$=164$
Hence the value of the expression ${\left(8+10\right)}^{2}$ is 324 and ${8}^{2}+{10}^{2}$ is 164

nick1337

Expert

Step 1
c) Given: $\left(a+b{\right)}^{2}={a}^{2}+{b}^{2}$
Use algebraic identity
$\begin{array}{}\left(x+y{\right)}^{2}={x}^{2}+2xy+{y}^{2}\\ \left(a+b{\right)}^{2}={a}^{2}+2ab+{b}^{2}\\ {a}^{2}+{b}^{2}={a}^{2}+{b}^{2}\\ \left(a+b{\right)}^{2}\ne {a}^{2}+{b}^{2}\end{array}$
Step 2
$\left(8+10{\right)}^{2}$
$={8}^{2}+2×8×10+{10}^{2}$
$=64+160+100$
$=324$
And
${8}^{2}={10}^{2}=64+100=164$
Hence the given relation is not true.

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