Question

Factorise : x3 - 49xy?​

Answer 1

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

(x3) - 72xy2

STEP

2

:

STEP

3

:

Pulling out like terms :

3.1 Pull out like factors :

x3 - 49xy2 = x • (x2 - 49y2)

Trying to factor as a Difference of Squares:

3.2 Factoring: x2 - 49y2

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 49 is the square of 7

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (x + 7y) • (x - 7y)

Final result :

x • (x + 7y) • (x - 7y)

hope it is helpful thank you stay happy stay safe stay healthy take care bye good night sweet dreams take care