Question

II Solve the following:
6. Factorize 4x2 – 9y2​

Answer 1

Answer:

Given

$4x {}^{2} - 9y {}^{2} \\ = (2x) {}^{2} - (3y) {}^{2}$

We know

$(a {}^{2} - b {}^{2} ) = (a + b)(a - b)$

Here

in given equation

$a = 2x \: \: \: \: and \: \: \: \: b = 3y$

So after putting value

$(2x) {}^{2} - (3y) {}^{2} \\ = (2x + 3y)(2x - 3y)$

I hope it will help.

Answer 2

answer is

(2x + 3y) • (2x - 3y)

Step-by-step explanation:

Changes made to your input should not affect the solution:

(1): "y2" was replaced by "y^2". 1 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

(4 • (x2)) - 32y2

STEP

2

:

Equation at the end of step

2

:

22x2 - 32y2

STEP

3

:

Trying to factor as a Difference of Squares

3.1 Factoring: 4x2-9y2

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 : 4 is the square of 2

Check : 9 is the square of 3

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (2x + 3y) • (2x - 3y)

Final result :

(2x + 3y) • (2x - 3y)