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Factorise 25x^(2) - 30xy + 9y^(2). The...

Factorise `25x^(2) - 30xy + 9y^(2)`.
The following steps are involved in solving the above problem . Arrange them in sequential order .
(A) `(5x - 3y)^(2) " " [ because a^(2) - 2b + b^(2) = (a-b)^(2)]`
(B) `(5x)^(2) - 30xy + (3y)^(2) = (5x)^(2) - 2(5x)(3y) + (3y)^(2)`
(C) `(5x - 3y) (5x - 3y)`

A

ABC

B

BCA

C

ACB

D

BAC

Text Solution

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The correct Answer is:
To factorise the expression \(25x^2 - 30xy + 9y^2\), we can follow these steps: ### Step 1: Identify the perfect square trinomial We start by recognizing that the expression can be related to the perfect square trinomial form \(a^2 - 2ab + b^2\). - Here, \(a = 5x\) and \(b = 3y\). - Therefore, we can rewrite the expression as: \[ (5x)^2 - 2(5x)(3y) + (3y)^2 \] ### Step 2: Write the expression in the perfect square form Now we can express the trinomial in the form of a square: \[ (5x - 3y)^2 \] ### Step 3: Write the final factorised form Thus, the factorisation of the expression \(25x^2 - 30xy + 9y^2\) is: \[ (5x - 3y)(5x - 3y) \quad \text{or simply} \quad (5x - 3y)^2 \] ### Summary of Steps 1. Recognize the expression as a perfect square trinomial. 2. Rewrite it in the form \((a - b)^2\). 3. Conclude with the factorised form.
To factorise the expression \(25x^2 - 30xy + 9y^2\), we can follow these steps: ### Step 1: Identify the perfect square trinomial We start by recognizing that the expression can be related to the perfect square trinomial form \(a^2 - 2ab + b^2\). - Here, \(a = 5x\) and \(b = 3y\). - Therefore, we can rewrite the expression as: \[ ...
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