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Factorise 28xy - 12x and y - 6x + 2xy - 3.

Mathematics

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Answers

2 parts
a

4x(7y - 3)

b

(y - 3)(1 + 2x)

Step-by-step solution

5 steps

Here are the factorisations.

Part a· 2 steps

Factorise 28xy−12x28xy - 12x.

  1. Find the greatest common factor (GCF) of the terms $28xy$ and $12x$.

    The GCF of the coefficients 28 and 12 is 4.
    The GCF of the variables xyxy and xx is xx.
    So, the GCF of 28xy28xy and 12x12x is 4x4x.

  2. Factor out the GCF from each term.

    28xy−12x=4x(7y)−4x(3)28xy - 12x = 4x(7y) - 4x(3) 28xy−12x=4x(7y−3)28xy - 12x = 4x(7y - 3)

    The answer is 4x(7y−3)\boxed{4x(7y - 3)}.

Part b(y - 3)(1 + 2x)

Factorise y−6x+2xy−3y - 6x + 2xy - 3.

  1. Group the terms to look for common factors.

    Rearrange the terms to group those with common factors:

    y−3−6x+2xyy - 3 - 6x + 2xy

    Group the first two terms and the last two terms:

    (y−3)+(−6x+2xy)(y - 3) + (-6x + 2xy)
  2. Factor out the common factor from each group.

    For the first group (y−3)(y - 3), the common factor is 1.

    1(y−3)1(y - 3)

    For the second group (−6x+2xy)(-6x + 2xy), the common factor is 2x2x.

    2x(−3+y)2x(-3 + y)

    So the expression becomes:

    1(y−3)+2x(y−3)1(y - 3) + 2x(y - 3)
  3. Factor out the common binomial factor (y−3)(y - 3).

    (y−3)(1+2x)(y - 3)(1 + 2x)

    The answer is (y−3)(1+2x)\boxed{(y - 3)(1 + 2x)}.

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