Question

(a + b)(a² - b²)=

What Is this answer??​

Answer 1

Answer:

Step-by-step explanation

A1=ab

A2=b²

A3=a (a-b) = a²-ab

A4=b (a-b) = ab-b²

Sixthly, Refer step 5, remove an above rectangle and a square which has areas as A1 and A2, after removing this, we have one rectangle and a square which have areas as A3, A4. For proving this formula, it is required to find out combined area of a rectangle (A3) and a square (A4), here, combined area can be called as A,

Hence,

A=A3+A4 ——————— (1)

A= (a + b) (a – b) ———— (2)

A3=a (a-b) = a²-ab ———- (3)

A4=b (a-b) = ab-b² ———- (4)

Balance the above areas,

A=A3+A4

(a + b) (a – b) = a²-ab + ab-b²

Cancel ‘ab’ from right hand side.

(a + b) (a – b) = a²– b²

Hence, it is proved.

Proof of (a + b) (a – b) = a²– b² by Numerical method:

For instance, if we take a= 4m and b=2m,

Hence,

a²– b²=(a + b) (a – b)

(4²-2²)=(4+2) (4-2)

16-4 = 6 X 2

12=12

LHS = RHS

Thus, it is proved.