Question

factorise a²x²-3abx+2b²=0

Answer 1

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Here's your answer...

a²x²-3abx+2b²
= a²x²-2abx+b²+b²-abx
= (ax-b)²-b(ax-b)
= (ax-b)(ax-b) - b(ax-b)
= (ax-b)(ax-b-b)
= (ax-b)(ax-2b)

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Answer 2

Hey!!


Given equation a^2x^2 - 3abx + 2b^2 = 0

On comparing with ax^2 + bx + c = 0 we get

a = a^2

b = - 3ab

c = 2b^2

In factorization method we know that the product of a and c should be the difference or sum of middle term



Middle term

- 3ab is written as

- abx - 2abx


Let's solve

$a {}^{2} x {}^{2} - 3abx + 2b {}^{2} = 0 \\ \\ = > a {}^{2} x {}^{2} - abx - 2abx + 2b {}^{2} = 0 \\ \\ = > ax(ax - b) - 2b(ax - b) = 0 \\ \\ = > (ax - b)(ax - 2b) = 0 \\ \\ = > ax - b = 0 \: \: or \: \: ax - 2b = 0 \\ \\ = > x = \frac{b}{a} \: \: or \: \: x = \frac{2b}{a}$



Hope it helps!