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Expand (3 – 2y)². Factorise 2x² - 3x + 1.

October 5, 2026Mathematics

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2 parts

9 - 12y + 4y^2

(2x - 1)(x - 1)

6 steps

Apply the formula for expanding a binomial squared, $(a-b)^2 = a^2 - 2ab + b^2$ .
Here, $a=3$ and $b=2y$ .
$(3 - 2y)^2 = (3)^2 - 2(3)(2y) + (2y)^2$
Simplify the terms.
$= 9 - 12y + 4y^2$
The expanded form is:
$\boxed{9 - 12y + 4y^2}$

Identify the coefficients of the quadratic expression $2x^2 - 3x + 1$ .
We need to find two numbers that multiply to $a \times c = 2 \times 1 = 2$ and add up to $b = -3$ . These numbers are $-1$ and $-2$ .
Rewrite the middle term using these two numbers.
$2x^2 - 2x - x + 1$
Factor by grouping the terms.
$2x(x - 1) - 1(x - 1)$
Factor out the common binomial factor $(x-1)$ .
$(2x - 1)(x - 1)$
The factorised form is:
$\boxed{(2x - 1)(x - 1)}$

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