Question

factorise 27x^2-75y^2​

Answer 1

factorise 27x^2-75y^2Answer:

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Equation at the end of step 1 :

(27 • (x2)) - (3•52y2)

Step 2 :

Equation at the end of step 2 :

33x2 - (3•52y2)

Step 3 :

Step 4 :

Pulling out like terms :4.1 Pull out like factors :

27x2 - 75y2 = 3 • (9x2 - 25y2)

Trying to factor as a Difference of Squares :

4.2 Factoring: 9x2 - 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 - B2Note : 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 : 25 is the square of 5

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (3x + 5y) • (3x - 5y)

Final result :

3 • (3x + 5y) • (3x - 5y)

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