Question

6. Factorise 27p^2x^2- 48 y^2​

Answer 1

Changes made to your input should not affect the solution:

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

Step by step solution :

Step 1 :

Equation at the end of step 1 :

((27 • (p2)) • (x2)) - (24•3y2)

Step 2 :

Equation at the end of step 2 :

(33p2 • x2) - (24•3y2)

Step 3 :

Step 4 :

Pulling out like terms :

4.1 Pull out like factors :

27p2x2 - 48y2 = 3 • (9p2x2 - 16y2)

Trying to factor as a Difference of Squares :

4.2 Factoring: 9p2x2 - 16y2

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 : 9 is the square of 3

Check : 16 is the square of 4

Check : p2 is the square of p1

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (3px + 4y) • (3px - 4y)

Final result :

3 • (3px + 4y) • (3px - 4y)

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