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

Verified Answer :

lukyo


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  \(\mathsf{(-7x+4)^2:}\)

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

     \(\mathsf{=49x^2-56x+16}\)        ✖

which is not a difference of squares.

—————

•  \(\mathsf{(-7x+4)\cdot (4-7x)}\)

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

     \(\mathsf{=49x^2-56x+16}\)        ✖

which is not a difference of squares.

—————

•  \(\mathsf{(-7x+4)\cdot (-7x-4)}\)

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

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

That is a difference of two squares.

—————

•  \(\mathsf{(-7x+4)\cdot (7x-4)}\)

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

     \(\mathsf{=-49x^2+56x-16}\)        ✖

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. =)

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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