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3 years ago

Factor completely 64x2– 49

Mathematics

2 answers:

Lady_Fox [76]3 years ago

5 0

The theorem is: a^2 - b^2 = (a+b) (a-b)
So, let's do this:

64x^2 - 49=
(8x)^2 - (7)^2=
(8x+7) (8x-7)

VARVARA [1.3K]3 years ago

3 0

Answer:

$(8x+7)(8x-7)$

Step-by-step explanation:

Rewrite the expression as:

$64x^2-49=(8x)^2-7^2$

We obtained a difference of two squares, so we can use the next formula:

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

In this case:

$a=8x$

and

$b=7$

Therefore:

$(8x)^2-7^2=(8x+7)(8x-7)$

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<em>Comment on the solution</em>

There are many ways you can go at the solution of this. The one you choose may depend on the kind of aritmetic you're comfortable with.

Since one of the dimensions is given in inches, and the result is required in feet, at some point you need to convert from inches to feet. It is useful to know that 12 inches equal 1 foot. That tells you that you can divide the number of inches by 12 to get the number of feet. (18 inches = 18/12 feet = 3/2 feet = 1 1/2 feet)

You can add the step lengths in inches (18 inches × 7 = 126 inches = 10 1/2 feet) or in feet (1 1/2 feet × 7 = 10 1/2 feet).

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Since one of the dimensions involves a fraction of a foot, at some point you have to deal with arithmetic involving fractions. Here, we have assumed you know how to do that (this is college math, after all).

Modern calculators are quite versatile in the sorts of expressions they can evaluate. For mine, it would be convenient to write it as ...

2×5+7×(18/12) . . . . would give 20 1/2

The Google search box is also a very good calculator for a variety of problems. Its use is shown below.

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