(x-5)^2 =? Squaring Binomials?

Question

Last question for the day! I swear! XD Sorry. This is my last worksheet anyway. (x-7)^2= ?

How do you do these? Can someone give me a rundown and how to do them? I guess you have to square them but I'm not getting it...

Answer 1

(x - 5)*(x - 5) = x^2 - 5x - 5x + 25 = x^2 - 10x + 25

not sure which you wanted, but i did the (x-5)^2 one.. follow suit for the (x-7)^2

Answer 2

While you could multiply (x-5)(x-5), there is a shortcut called the squares of binomials. It is:

(a+b)²= a²+2ab+b² or (a-b)²= a²-2ab+b²

Apply it to (x-5)²

(x-5)²= x²-2(5x)+5²= x²-10x+25

Answer 3

Question 1
(x - 5).(x - 5) = x² - 5x - 5x + 25 = x² - 10x + 25

Question 2
(x - 7).(x - 7) = x² - 7x - 7x + 49 = x² - 14x + 49

Answer 4

Okay, I'd love to help..

Now in order to multiply a binomial by another binomial or square a bionomial, you have to use FOIL.

(x-5)(x-5)

Use FOIL
F-multiply first terms (x)(x)
O-multiply outer terms- (x)(-5)
I- multiply inner terms - (-5)(x)
L- multiply last terms- (-5)(-5)

No we get a new equation. x^2 -10x+25.

Get it?

There's also another formula for squaring a bionomial but not multiplying two by each other.

It is (a-b)^2= a^2-2ab+b^2

And this formula checks our answer to be correct!

Hope I helped!

Answer 5

note
(x - 7)^2 is a perfectly squared binomial

Take the first term "x" and square it which will be the first term
The second term will be two times the product of the inside terms
2*(x*-7) = -14x
Take the second term "-7" and square it, which will be the last term

x^2 - 14x + 49

Answer 6

(x - 5)^2
= (x - 5)(x - 5)
Multiply each term in the first bracket by each term in the second bracket, and add the results:
Firsts: x*x = x^2
Outsides: - 5*x =-5x
Insides: -5*x = -5x
Lasts: (-5)*(-5) = 25
x^2 - 5x - 5x + 25
= x^2 - 10x + 25.

Similarly with (x - 7)^2
to get:
x^2 - 14x + 49.

Answer 7

x^4 -- x^2 -- 12 ...... here --12 = (--4)(3) and -- 4 + 3 = -- 1 = x^4 -- 4x^2 + 3x^2 -- 12 = x^2(x^2 -- 4) + 3(x^2 -- 4) = (x^2 -- 4)(x^2 + 3) y^2 + 9y -- 52 .........here --52 = (13)(--4) and 13 -- 4 = 9 = y^2 + 13y -- 4y -- 52 = y(y + 13) -- 4(y + 13) = (y + 13)(y -- 4) 25x^2 -- 64y^2 = (5x)^2 -- (8y)^2 = (5x + 8y)(5x -- 8y) x^2 -- (y -- 2)^2 = (x + y -- 2)(x -- y + 2) x^5 + 3x^4 -- x -- 3 = x^4(x + 3) -- 1(x + 3) = (x + 3)(x^4 -- 1) = (x + 3)(x^2 + 1)(x^2 -- 1) = (x + 3)(x^2 + 1)(x + 1)(x -- 1) 6s^2 + 19s -- 77 = 6s^2 + 33s -- 14s -- 77 = 3s(2s + 11) -- 7(2s + 11) = (2s + 11)(3s -- 7)

Answer 8

You should definitely understand *why* the above answers are true. Once you do, you can use this shortcut.

(x+c)^2 = x^2 + 2cx + c^2
(x-c)^2 = x^2 - 2cx + c^2

This is essentially a rephrasing of previous answers, but it gives you an explicit formula for plugging in values of c.

Answer 9

(x-5)^2
is the same thing as (x-5) * (x-5)
now open up the brackets and expand

= x * (x-5) - 5 * (x-5)
= x*x - x*5 - 5*x - 5*(-5)
= x^2 - 10x + 25


Similarly u can work out
(x-7)^2

answer is
x^2 - 14x + 49

All the Best!! :)

Answer 10

(X-5)^2
using the diff formula
(a-b)^2=a^2-2ab+b^2,we have
(x-5)^2=x^2-2.x.5+5^2
=x^2-10x+25
So solve( x-7)^2???
Pl remember formulas ,they can get you to the TOP.