use the identies : (a+b)^2 = (a^2+2ab+b^2) and (a-b)^2 = (a^2-2ab+b^2) to evaluate the square of the number 53,96,105,99 and 109 . you have to choose any of the two identities which you think to be suitable to find the square of any number.
Answers
Step-by-step explanation:
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
Answer:
use (x+a)(x+b)
(100+9)(100+539610499)