Question

factorize 3a^2-18ab+12ab^2​

Answer 1

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Answer 2

Answer:

3a(a-6b+4b^2)

or

[a - b(3 + √5)][a - b(3 - √5)] = 0

Step-by-step explanation:

3a^2-18ab+12ab^2​ cannot be factorised because of the last term 12ab^2 which has an unwanted a

Still, if you want it to be factorised with a, then it's easy:

3a(a-6b+4b^2)

But if that was a mistake in your typing, then

Ignoring the term a in the last term, we will get 3a^2-18ab+12b^2

Divide by 3 to get 3(a^2-6ab+4b^2)

This is a type of quadratic equation of the type ax² + bx + c = 0 with a instead of x as the variable.

where a = 1, b=-6b, c=4b²

Using the quadratic formula, we get a= [6b±√(36b² - 16b²)]/2

a= [6b±√20b²]/2

= [6b±2√5b]/2

= 2(3b±√5b)/2

= b(3±√5)

or a = b(3 + √5) OR a = b(3 - √5)

∴ a - b(3 + √5) = 0 OR a - b(3 - √5) = 0

Hence the factors are [a - b(3 + √5)][a - b(3 - √5)] = 0