Help with Algebra 1 Homework?

Question

Simplify expression....

(4+squareroot of 7)(4-squareroot of 7)

Answer 1

In order to simplify this expression, you want to use the FOIL method to multiply each of the terms with one another, and from there you can try to combine like terms and simplify if possible:

(4 + √7)(4 - √7)
16 - 4√7 + 4√7 - 7
16 - 7
= 9

When you square a square root, which you did for the two last terms, both actions cancel one another out, and your left with the number of value in the radicand on its own, which in this case is just 7. Since the problem involved a difference of squares, thet two middle terms also cancel out, and therefore, you should get an answer of 9. Hope that helps!

Answer 2

Just took Calculus good sir.

Although you should ideally ask your teacher, the short answer to your question is:

1. Do the method known as foiling (that's multiply the 4 together so you get 16

Here's your equation so far:

16 .

2. Bear with me please. Now you do the 4 times squareroot of 7 so you get:

16- 4 x root 7

3. Then you do the same for the rest so you get:

16 - (4 x root 7) + (root 7 x 4) - 7 (because the square of
two square roots is 7.

So, to repeat:

16 - (4 x root 7) + (root 7 x 4) - 7 = x
X= The Answer

So if you solve that you should be fine. Sounds like you're in beginning algebra. As someone who just went through the horror that is college calculus I might be able to help you. Like I said, ideally talk to the teacher but if they're no help you can just E-mail me. So there you go dude.

Answer 3

(4+squareroot of 7)(4-squareroot of 7)

1st you multiply the 1st term in the 1st bracket by the other terms in the second bracket.
2nd you multiply the 2nd term in the 1st bracket by the other terms in the second bracket.

Remember:
+ multiplied by +, and - multiplied by - would both give a +
+ multiplied by -, and - multiplied by + would both give a -

So (4 x 4) - (4 x squareroot 7) + (4 x squareroot 7) - (squareroot 7 x squareroot 7)
= 16 - (squareroot 7)^2)
= 16 - 7
= 9

Answer 4

(4 +√7).(4 - √7)
= 16 - 4.√7 + 4√7 - 7
= 9

Answer 5

forget the squareroot of 7 for now
use FOIL
(4+a)(4-a)
16 -4a +4a -a(squared)
16 -a(squared) (...which is 7 by the way)
16 - 7 = 9

Answer 6

this is a difference of two squares:

using the formula (a+b)(a-b) = a^2-b^2 gives `16-7 = 9

your expression simplifies to 9

Answer 7

(4 + √7)(4 - √7 =

16 + 4√7 - 4√ - √7√7 =

16 - √49 =

16 - 7 =

9

- - - - - - - - -s-

Answer 8

(4 + squareroot of 7) (4 - squareroot of 7)
4 + 2.7 x 4 - 2.7
6.7 x 1.3 = 8.71 or 9 ??
(rounded)

Answer 9

(4+√7)(4-√7)

Use the FOIL method!

16 - 4√7 + 4√7 - √49
16 - 0 - 7 = 9

Answer 10

There's a couple of ways to look at this -

1) Just distribute (or FOIL method it's sometimes called) then combine like terms. You'll see that the middle terms drop and you'll be able to simplify the radical and add the values.

2) If you are familiar with conjugates, then these are conjugates. When you multiply them, you'll get the "difference of squares".

Hope this helps!