Question

find the product of following using properties of square.
(a)
$13 \times 15$
(b)
$28 \times 30$
( c )
$53 \times 55$
( d )
$100 \times 102$
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Answer 1

Step-by-step explanation:

$\sf Identity : ( a + b )( a - b) = {a}^{2} + {b}^{2} \\ \\ \sf (a)\: 13 × 15 \\ \\ \sf \longrightarrow (14-1)(14+1) \\ \\ \sf \longrightarrow {14}^{2} -{1}^{2} \\ \\ \sf \longrightarrow 196- 1 \\ \\ \sf \longrightarrow 195 \\ \\ \sf (b) \: 28 × 30 \\ \\ \sf \longrightarrow (29-1)(29+1) \\ \\ \sf \longrightarrow {29}^{2}-{1}^{2} \\ \\ \sf \longrightarrow 861 - 1 \\ \\ \sf \longrightarrow 860 \\ \\ \sf (c)\:53×55 \\ \\ \sf \longrightarrow (54-1)(54+1) \\ \\ \sf \longrightarrow {54}^{2} - {1}^{2} \\ \\ \sf \longrightarrow 2916 - 1 \\ \\ \sf \longrightarrow 2915 \\ \\ \sf (d)\:100 × 102 \\ \\ \sf \longrightarrow (101-1)(101+1) \\ \\ \sf \longrightarrow {101}^{2} - {1}^{2} \\ \\ \sf \longrightarrow 10201 - 1 \\ \\ \sf \longrightarrow 10200$

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