Question

Factorize: 48x² - 75y²​

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

(48 • (x2)) - (3•52y2)

STEP

2

:

Equation at the end of step

2

:

(24•3x2) - (3•52y2)

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

48x2 - 75y2 = 3 • (16x2 - 25y2)

Trying to factor as a Difference of Squares:

4.2 Factoring: 16x2 - 25y2

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 : 16 is the square of 4

Check : 25 is the square of 5

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (4x + 5y) • (4x - 5y)

Final result :

3 • (4x + 5y) • (4x - 5y)

Answer 2

Answer:

3(4x-5 y) (4 x + 5 y)

Step-by-step explanation:

hope it helps..