Factorise using formula (a²+b²)=(a+b)(a-b)
1:- 100³-x
Answers
Step-by-step explanation:
Its algebra…..and algebra is nothing but taking variable instead of comstants……
In elementary algebra, difference of squares is defined as: The subtraction of two squares terms is a squared term minus from another squared term i.e. x2 2 - y2 2 .
This may be factored according to the given below mathematical identity.
x2 2 - y2 2 = (x - y)(x + y)
Here x2 2 - y2 2 expression is called a difference of two squares. And (x - y) and (x + y) are the factors of x2 2 - y2 2 .
Rule for factoring the difference of two squares:
Difference of two squares = Sum of two numbers multiplies their difference.
i.e. x2 2 - y2 2 = (x - y)(x + y)
Proof..
The proof of this identity is very simple. Let us apply distributive property on the right hand side.
(m - n)(m + n) = m2 m2 + mn - nm + n2 n2 .............(1)
Put mn - nm = 0 (Application of commutative property)
For two variables above result gives a simple proof of AM-GM inequality. This result is commonly used in mathematics. Also it will hold in any commutative ring.
Conversely, if this identity holds in a ring then that ring is commutative. To verify this, apply distributive property to the right hand side of equation (1).
m2 m2 + mn - nm + n2 n2 , for this is equal to m2 m2 - n2 n2 we must have mn - nm = 0.
It means ring is commutative.
Difference of two perfect squares is given below:
Difference of two perfect squares = Sum of two numbers × × Difference of two numbers
m2 2 - n2 2 = (m - n)(m + n)Alternate method:
We can also proof this formula from direct calculation.
Solve (m - n)(m + n) using FOIL method
m2 m2 + mn - nm + n2 n2
m2 m2 + mn - mn + n2 n2
m2 m2 - n2 n2 (cancel out common terms)
The difference of two squares formula is valid for real numbers and for complex numbers.