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boyakko [2]
3 years ago
13

Which of the following is a perfect square trinomial?

Mathematics
2 answers:
yanalaym [24]3 years ago
6 0
Your answer is D. 16x² - 56xy + 49y².

A perfect square trinomial is the result of a squared binomial, like (a + b)². Using this example, the perfect square trinomial would be a² + 2ab + b², as that is what you get when you expand the brackets.

Therefore, to determine which of these is a perfect square trinomial, we have to see if it can be factorised into the form (a + b)².

I did this by first square rooting the 16x² and 49y² to get 4x and 7y as our two terms in the brackets. We automatically know the answer isn't A or B as you cannot have a negative square number.

Now that we know the brackets are (4x + 7y)², we can expand to find out what the middle term is, so:

(4x + 7y)(4x + 7y)
= 16x² + (7y × 4x) + (7y × 4x) + 49y²
= 16x² + 28xy + 28xy + 49y²
= 16x² + 56xy + 49y².

So we know that the middle number is 56xy. Now we assumed that it was (4x + 7y)², but the same 16x² and 49y² can also be formed by (4x - 7y)², and expanding this bracket turns the +56xy into -56xy, forming option D, 16x² - 56xy + 49y².

I hope this helps!
AVprozaik [17]3 years ago
6 0

Answer:

It would have to be the last choice

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Complete the work to find the dimensions of the rectangle. x(x – 3) = 10 x2 – 3x = 10 x2 – 3x – 10 = 10 – 10 (x + 2)(x – 5) = 0
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Step-by-step explanation:

Given

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See comment for missing part of the question

Required

Complete the expression to determine the dimension of a rectangle

We have:

x(x-3) =10

Open bracket

x^2 -3x = 10

Equate to 0

x^2 -3x - 10 =0

Expand

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Factorize

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Solve for x

x - 5 = 0 or x + 2 = 0

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The value of x cannot be negative

So:

x  = 5

Recall that:

Length = x

Width = x - 3

So:

Length =5

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