Question

factorise the following. ​

Answer 1

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

((22•3x2) • y2) - 300

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

12x2y2 - 300 = 12 • (x2y2 - 25)

Trying to factor as a Difference of Squares:

3.2 Factoring: x2y2 - 25

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 : 25 is the square of 5

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (xy + 5) • (xy - 5)

Final result :

12 • (xy + 5) • (xy - 5)