1+2ab-(a²+b²) solve
Answers
Step-by-step explanation:
Factorization of the expression 1-2 a b-\left(a^{2}+b^{2}\right)1−2ab−(a
2
+b
2
) is
\bold{(1+a+b) (1-a-b)}(1+a+b)(1−a−b)
Given:
1-2 a b-\left(a^{2}+b^{2}\right)1−2ab−(a
2
+b
2
)
To Find:
Factorization of 1-2 a b-\left(a^{2}+b^{2}\right)1−2ab−(a
2
+b
2
)
Solution:
The given expression is,
1-2 a b-\left(a^{2}+b^{2}\right)1−2ab−(a
2
+b
2
)
Now, the above expression can be written as
1-\left(a^{2}+b^{2}+2 a b\right)1−(a
2
+b
2
+2ab)
The above expression can be written as,
=1-(a+b)^{2}\left[\because(a+b)^{2}=a^{2}+b^{2}+2 a b\right]=1−(a+b)
2
[∵(a+b)
2
=a
2
+b
2
+2ab]
Now, we get
=(1)^{2}-(a+b)^{2}\left[\text { Since, } 1=1^{2}\right]=(1)
2
−(a+b)
2
[ Since, 1=1
2
]
Now, on expanding the above equation, the new expression is,
=[1+(a+b)][1-(a+b)]=[1+(a+b)][1−(a+b)]
Now, the equation becomes,
=(1+a+b)(1-a-b)=(1+a+b)(1−a−b)