Question

Find 106²,108²,116² by using identity.

Answer 1

Find 106²,108²,116² by using identity.

Good question,

Here is your perfect answer!

1) (106)²

= (100+6)²

= 100² + 6² + 2(100*6)

= 11236

2) (108)²

= (100+8)²

= 100² + 8² + 2(100*8)

= 11664.

3) (116)²

= (100+16)²

= 100² + 16² + 2(100*16)

= 10000 + 256 + 3200

= 13456.

Answer 2

$\textbf {Solution }$

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${106}^{2} \\ = > ( 100 + 6)^{2}$
Using identity
$(a + b) ^{2} = {a}^{2} + {b}^{2} + 2ab$
${(100 + 6)}^{2} \\ = > {100}^{2} + {6}^{2} + 2 \times 100 \times 6 \\ = > 10000 + 36 + 1200 \\ = > 11236$
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${108}^{2} \\ = > {(100 - 8)}^{2}$
Using identity

$(a + b) ^{2} = {a}^{2} + {b}^{2} + 2ab$
${(100 + 8)}^{2} \\ = > {100}^{2} + {8}^{2} + 2 \times 100 \times 8 \\ = > 10000 + 64 + 1600 \\ = > 11664$
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${116}^{2} \\ = > (120 - 4)^{2}$
Using identity

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

${(120 - 4)}^{2} \\ = > {120}^{2} + {4}^{2} - 2 \times 120 \times 4 \\ = > 14400 + 16 - 960 \\ = > 14416 - 960 \\ = > 13456$
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$\textbf{Thanks}$