Question

factorise a³-2root2b³+3root 3c³+3root 6abc​

Answer 1

STEP

1

:

Equation at the end of step 1

(((a2) • (b2)) - 6abc) + 32c2

STEP

2

:

Trying to factor a multi variable polynomial

2.1 Factoring a2b2 - 6abc + 9c2

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

Found a factorization : (ab - 3c)•(ab - 3c)

Detecting a perfect square :

2.2 a2b2 -6abc +9c2 is a perfect square

It factors into (ab-3c)•(ab-3c)

which is another way of writing (ab-3c)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 :

(ab - 3c)2

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