Question

The expanded form of (√3x – 2y)^2 is​

Answer 1

Answer:

The expanded form of expression (3x - 2y)2 is ( 9x2 + 4y2 - 12xy).

Answer 2

Given: The expression is  (√3x – 2y)²

To find The expanded form of the above expression

Solution: For solving the above expression, we have to implement a formula used in the study of algebra and that is (a-b)²=a²-2ab+b², this formula is used in the binomial term when the term is squared and it is actually expanding the term or expression. This formula is proved both geometrically and algebraically.

Here we can consider for the given expression that a=(√3x), b=2y

∴ Implementing the formula (a-b)²=a²-2ab+b² to the given expression

(√3x – 2y)², we have

{(√3x)²-(2×√3x×2y)+(2y)²}

= {(√3)²x²-4√3xy+(2)²y²}

=3x²-4√3xy+4y²  [∵ squaring any root number gets a result of the number without the root, so (√3)²=3]

Hence the expanded form of (√3x – 2y)² is 3x²-4√3xy+4y².