4. Factor (2a – b)^2- 4a^2

(-b) (4a-b)

Step-by-step explanation:

(2a – b)^2- 4a^2

Let m = 2a-b

m^2 - (2a)^2

We know this is the difference of squares

x^2 - y^2 = (x-y)(x+y)

(m-2a) (m+2a)

Replace m with 2a -b

(2a -b-2a) (2a-b+2a)

Simplify

(-b) (4a-b)

(4a - b)(-b)

Step-by-step explanation:

If we let x = 2a - b and y = 2a, our expression now looks like

This kind of a expression is a common pattern in algebra called a difference of squares, and it can be factored like this (for a visual proof, see the attached image, courtesy of Great Maths Teaching Ideas):

Replacing x and y with 2a -b and 2a, our expression now becomes

So in factored form,

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step-by-step explanation: