Question

Simplify the following expressions: (2x-1)² – (x-1)²​

Answer 1

Answer:

2x^2+1-4x-x^2-1+2x

x^2-2x

x(x-2)

Step-by-step explanation:

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Answer 2

The simplified expression is x(x-2).

Given - Expression

Find - Simplification

Solution - As we can see, the given expressions represent (a - b)² form. We are also aware by its expansion, which is: a² + b² - 2ab.

So, expanding the given expression in above form -

Expression = (2x² + 1² - 2×2x×1) - (x² + 1² - 2×x×1)

Performing multiplication in expression

Expression = (2x² + 1 - 4x) - (x² + 1 - 2x)

Subtracting the values

Expression = x² + 0 - 2x

Expression = x² - 2x

Further simplifying the expression

Simplified expression = x (x - 2)

Hence, the simplified value of expression is x(x-2).

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