Question

34. 1 - 2ab - (a? + b2 =?
a) (+ a + b) (1 + a + b)
b) (1 + a + b)(1 - a + b)
c) (1 + a + b)(1-a -b)
d) (1 + a - b)(1 - a +b)

Answer 1

Answer:

1-2ab-(a²+b²)

=1-(2ab+a²+b²)

=1-(a+b)²

We know that x²-y²=(x-y)(x+y)

In the equation we got, x=1 and y=(a+b)

1²-(a+b)²=(1-a-b)(1+a+b)

Answer 2

Answer:

Factors of 1-2ab-(a²+b²) ➠ (1+a+b)(1-a-b)

Given

1-2ab-(a²+b²)

➩ 1-2ab-a²-b²

➩ 1-(2ab+a²+b²)

➩ 1-(a+b)²

[ By algebraic identity : x²+y²+2xy =(x+y)² ]

➩ $\sf{1² - ( a + b )²}$

➩ $\sf{[ 1 + ( a + b ) ][ 1 - ( a + b )]}$

[ By algebraic identity: x²-y² =(x+y)(x-y) ]

➩ $\sf\red{( 1 + a + b )( 1 - a - b )}$

$\tt{\therefore 1 - 2ab - ( a²+ b²) = (1+a+b)(1-a-b)}$

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