Question

factorize 2x^2 - 98y^2

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

(2 • (x2)) - (2•72y2)

STEP

2

:

Equation at the end of step

2

:

2x2 - (2•72y2)

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

2x2 - 98y2 = 2 • (x2 - 49y2)

Trying to factor as a Difference of Squares:

4.2 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 :

2 • (x + 7y) • (x - 7y)

Answer 2

2x² - 98y²

⇒ 2 ( x² - 49y² )

⇒ 2 ( x + 7y ) ( x - 7y )