Question

(4w-3)^2
what would be the answer to that?? please explain, i’m so confused.

Answer 1

Answer: 16w^2 - 24w + 9

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Step-by-step explanation:

(4w-3)^2 is the same as (4w-3)(4w-3) because squaring something is the same as multiplying it by itself.

Another example would be something like 7^2 = 7*7

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So we're asked to expand out (4w-3)(4w-3)

Let's make x = 4w-3 and replace that first copy of '4w-3' with 'x'

We get this expression: x(4w-3)

Distribute the x through to get...

x(4w-3)

x*4w + x*(-3)

4wx - 3x

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Now replace the x with (4w-3) and apply distribution twice more

4wx - 3x

4w(4w-3) - 3(4w-3)

16w^2 - 12w - 12w + 9

16w^2 - 24w + 9 which is the answer

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You can use the FOIL rule as an alternative method to get this answer. The box method is a visual tool to keep all the terms organized. See the attached image below for what I mean by the box method. The four terms inside the boxes represent the four terms from 16w^2 - 12w - 12w + 9, which was the second to last step we got shown above.

Yet another alternative you could use is the perfect square formula which is

(a-b)^2 = a^2 - 2ab + b^2

where in this case, a = 4w and b = 3.

Answer 2

16w^2 - 24w + 9

Step-by-step explanation:

To simplify this, you would use the special product (a - b)^2 = a^2 - 2ab + b^2. We can correlate this with the given term so that,

a = 4w

and

b = 3

Now we just substitute into a^2 - 2ab + b^2

(4w)^2 - 2(4w)(3) + (3)^2

16w^2 - 24w + 9