Evaluate using suitable identity (99)²
Answers
Answer:
An identity is true only for certain values of its variables. An equation is not an identity.
The following are the identities
(a + b)² = a² + 2ab + b²
(a – b)² = a² – 2ab + b²
(a – b)(a + b) = a² – b²
Another useful identity is
(x + a) (x + b) = x² + (a + b) x + ab
If the given expression is the difference of two squares we use the formula
a² –b² = (a+b)(a-b)
• The above four identities are useful in carrying out squares and products of algebraic expressions. They also allow easy alternative methods to calculate products of numbers and so on.
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Solution:
1) 99²
= (100 -1)²
= 100²- 2×100×1 + 1² [(a – b)² = a² – 2ab + b² ]
= 10000 - 200 + 1
= 9801
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(99)²=(100-1)²
=Applying (a-b)²
=(100)²+(1)²-2(100)(1)
=10000+1-200
=9801