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2 months ago

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

2 answers:

8 0

To identify a difference of squares, you can expand each expression and check if it meets that criterion.

• $\mathsf{(-7x+4)\cdot (-7x+4)}$

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 does not represent 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.

—————

• $\mathsf{(-7x+4)\cdot (-7x-4)}$

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

$\mathsf{=(7x)^2-4^2}$ ✔

This is indeed 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 does not result in a difference of squares.

—————

Only the third choice will yield a difference of squares.

Conclusion: (− 7x + 4) · (− 7x − 4).

I trust this information is helpful. =)

babunello [11.8K]2 months ago

3 0

Conclusion:

The expression resulting in a difference of two squares is:

(–7x + 4)·(–7x – 4)

Detailed explanation:

We can recall that the formula for this type of expression is:

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

indicating it's a difference of two squared quantities (a^2 and b^2)

Thus, the expression that fulfills this criteria is:

(-7x + 4)·(-7x-4)

As,

here $a=-7x$ and $b=4$ and

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

confirming the expression constitutes a difference of two square values:

$(7x)^2$ and $4^2$

Thus, the accurate answer is:

(-7x + 4)·(-7x-4)

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