Question

Factorise: 12x^2 - 75y^2 = 3 (yx^2 - 25y^2)​

Answer 1

Step by Step Solution

STEP 1 : Equation at the end of step 1

(12 • (x2)) - (3•52y2)

STEP 2 :

Equation at the end of step 2 :

(22•3x2) - (3•52y2)

STEP 3 :

STEP4:

Pulling out like terms

4.1 Pull out like factors :

12x2 - 75y2 = 3 • (4x2 - 25y2)

Trying to factor as a Difference of Squares:

4.2 Factoring: 4x2 - 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 : 4 is the square of 2

Check : 25 is the square of 5

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (2x + 5y) • (2x - 5y)

Final result :

3 • (2x + 5y) • (2x - 5y)

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