Question

Simplyfy the following using :
$(a + b)(a - b) = a ^2 - b^2 (a)68 \times 72 \: \: (b)101 \times 99 \: \: \: (c)67 \times 73$
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Answer 1

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$\mathfrak{Simplify\: the \:following\: using}$ $\purple{\boxed{\bf{\orange{a²\:-\:b²}}}}$

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a} $68 \times 72$

$\implies ( 70\:-\:2 ) ( 70\:+\:2 )$

$\implies ( 70\:+\:2 ) ( 70\:-\:2 )$

$\implies ( 70 ) ^{2} - ( 2 ) ^{2}$

$\implies 4900\:-\:4$

$\implies 4896$

b} $101 \times 99$

$\implies ( 100\:+\:1 ) ( 100\:-\:1 )$

$\implies ( 100 ) ^{2} - ( 1 ) ^{2}$

$\implies 10000\:-\:1$

$\implies 9999$

c} $67 \times 73$

$\implies ( 70\:-\:3 ) ( 70\:+\:3 )$

$\implies ( 70\:+\:3 ) ( 70\:-\:3 )$

$\implies ( 70 ) ^{2} - ( 3 ) ^{2}$

$\implies 4900\:-\:9$

$\implies 4891$

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