Question

Factorise 9x^3-24x^2y+16xy^2

Answer 1

Answer:

9x3-24x2y+16xy2

Final result :

x • (3x - 4y)2

Step by step solution :

Step 1 :

Equation at the end of step 1 :

((9•(x3))-((24•(x2))•y))+24xy2

Step 2 :

Equation at the end of step 2 :

((9 • (x3)) - ((23•3x2) • y)) + 24xy2

Step 3 :

Equation at the end of step 3 :

(32x3 - (23•3x2y)) + 24xy2

Step 4 :

Step 5 :

Pulling out like terms :

5.1 Pull out like factors :

9x3 - 24x2y + 16xy2 = x • (9x2 - 24xy + 16y2)

Trying to factor a multi variable polynomial :

5.2 Factoring 9x2 - 24xy + 16y2

Try to factor this multi-variable trinomial using trial and error

Found a factorization : (3x - 4y)•(3x - 4y)

Detecting a perfect square :

5.3 9x2 -24xy +16y2 is a perfect square

It factors into (3x-4y)•(3x-4y)

which is another way of writing (3x-4y)2

How to recognize a perfect square trinomial:

• It has three terms

• Two of its terms are perfect squares themselves

• The remaining term is twice the product of the square roots of the other two terms

Final result :

x • (3x - 4y)2