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Leno4ka [110]
3 years ago
10

Which will result in a difference of squares? (–7x + 4)(–7x + 4) (–7x + 4)(4 – 7x) (–7x + 4)(–7x – 4) (–7x + 4)(7x – 4)

Mathematics
2 answers:
maw [93]3 years ago
8 0

You can simply expand each product and see whether it gives you a difference of squares.


•  \mathsf{(-7x+4)\cdot (-7x+4)}

That's actually  \mathsf{(-7x+4)^2:}

     \mathsf{(-7x+4)^2}\\\\ \mathsf{=(-7x+4)\cdot (-7x+4)}\\\\ \mathsf{=(-7x+4)\cdot (-7x)+(-7x+4)\cdot 4}\\\\ \mathsf{=49x^2-28x-28x+16}

     \mathsf{=49x^2-56x+16}        <span>✖

which is not a difference of squares.

</span>————<span>—

</span>•  \mathsf{(-7x+4)\cdot (4-7x)}

     \mathsf{=(-7x+4)\cdot 4-(-7x+4)\cdot 7x}\\\\ \mathsf{=-28x+16-(-49x^2+28x)}\\\\ \mathsf{=-28x+16+49x^2-28x}

     \mathsf{=49x^2-56x+16}        ✖

which is not a difference of squares.

—————

•  \mathsf{(-7x+4)\cdot (-7x-4)}

     \mathsf{=(-7x+4)\cdot (-7x)-(-7x+4)\cdot 4}\\\\ \mathsf{=49x^2-28x-(-28x+16)}\\\\ \mathsf{=49x^2-\diagup\!\!\!\!\! 28x+\diagup\!\!\!\!\! 28x-16}\\\\ \mathsf{=49x^2-16}

     \mathsf{=(7x)^2-4^2}        <span>✔

That is a difference of two squares.

</span>————<span>—

</span>•  \mathsf{(-7x+4)\cdot (7x-4)}

     \mathsf{=(-7x+4)\cdot 7x-(-7x+4)\cdot 4)}\\\\ \mathsf{=-49x^2+28x-(-28x+16)}\\\\ \mathsf{=-49x^2+28x+28x-16}

     \mathsf{=-49x^2+56x-16}        <span>✖

</span>which is not a difference of squares.

—————

Only the  third option  will result in a difference of squares.


Answer:  (− 7x + 4) · (− 7x − 4).


I hope this helps. =)

Law Incorporation [45]3 years ago
3 0

Answer:

The expression which will result in difference of two squares is:

(–7x + 4)·(–7x – 4)

Step-by-step explanation:

We know that the formula of the type:

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

i.e. it is a difference of two square quantities. (a^2 and b^2)

Hence the option which satisfies the following expression is:

(-7x + 4)·(-7x-4)

since,

here a=-7x and b=4 and

(-7x+4).(-7x-4)=(-7x)^2-(4)^2=(7x)^2-4^2

so the expression is a difference of two square quantities:

(7x)^2 and 4^2

Hence, the correct answer is:

(-7x + 4)·(-7x-4)

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8 0
2 years ago
Please help (-0.5)/(-0.5 ) -50/(-0.5 )
Kipish [7]
If you would like to solve (- 0.5) / (- 0.5) and - 50 / (- 0.5), you can do this using the following few steps:

(- 0.5) / (- 0.5) = 0.5 / 0.5 = 1

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</span>
The correct results would be: (- 0.5) / (- 0.5) = 1 and - 50 / (- 0.5<span>) = 100.</span>
6 0
3 years ago
8) The height of a building h varies directly as the length and inversely as the width, if h = 25m when l = 10m and w = 5m, find
shtirl [24]

Let h,l, and w represent the height, length, and width of the building respectively

Then

\begin{gathered} h\text{ = }\frac{kl}{w} \\ \text{where k is the constant of proportionality} \end{gathered}\begin{gathered} \Rightarrow k=\frac{hw}{l} \\ \Rightarrow k=\frac{25\times5}{10}=12.5 \end{gathered}\Rightarrow h=\frac{12.5l}{w}

The new value of h = 50m, but l remains the same.

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\begin{gathered} \frac{50}{1}=\frac{12.5\times10}{w} \\ \Rightarrow\frac{50}{1}=\frac{125}{w} \\ \text{Cross multiplying, we have} \\ 50w\text{ = 125} \\ \Rightarrow\text{ w=}\frac{125}{50}=2.5 \end{gathered}

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inessss [21]
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Nikolay [14]

Answer:

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Step-by-step explanation:

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8 0
1 year ago
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