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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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One number is nine more than a second number. Four times the first is 6 less than 2 times the second. Find the numbers.
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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3 years ago
Which is equivalent to 64 to the 1/4 power
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Answer:

The answer to your question is the first option

Step-by-step explanation:

                                            64^{1/4}

Process

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                                      64  2

                                      32  2

                                      16   2

                                        8  2

                                        4  2

                                        2  2

                                         1

                      64 = 2⁶

2.- Express 64 as a fractional exponent

                      64^{1/4} = 2^{6/4}

3.- Simplify

                      64^{1/4} = 2^{4/4} 2^{2/4}

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4.- Result

                      64^{1/4} = 2\sqrt[4]{4}                                        

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