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,

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b