Question

Simplify the following using identifies. (Grade 8)

1. (109)²+(91)² =

2. (200)²–(100)² =

Answer 1

Hii miss,

1. (109)² + (91)²
= (100+9)²+(100-9)²
= 100²+2(100)(9)+9²+100²-2(100)(9)+9²
= 10000+1800+81+10000- 1800+81
= 20162
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2. (200)²- (100)²
= (200+100)(200-100)
= 300*100
=30000
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HOPE THIS HELPS U...☺

Answer 2

1. (109)² + (91)²

= (100+9)² + (100-9)²

= 100²+ 9² + 2(100)(9) + 100²+9²-2(100)(9)

[ Identity used -
(a+b)² = a²+b²+2ab
(a-b)² = a²+b²-2ab ]

= 10000+81+1800+10000+81-1800

= 20000+162

=20162

2. (200)²-(100)²

=(200+100)(200-100)

[ Identity used -
a²-b² = (a+b) ( a-b) ]

= 300×100

= 30000