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# Squaring a binomial (old)

An old video where Sal expands and simplifies (7x+10)². Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• Where is he getting 140x from?
Thanks.
• 49x^2+70x+70x+100, simply add the 70x+70x = which is 140x
• I thought that with powers to powers you distributed the exponent to the exponents inside the parenthesis? Hence...

(x+3)^2=x^2+3^2=x^2+9

Why is this not true?
• Because:
1.) We need to follow the order of operations P.E.M.D.A.S
2.) A set of numbers inside a parenthesis is considered as a single number itself.
To see how it works using numbers instead of variables may make things clearer for us.
Lets substitute x by 5 and see what happens when we follow P.E.M.D.A.S.
(5+3)^2
=25+2(5)3+9
or 8^2 → I followed the order of operations P.E.M.D.A.S, I first did the operation inside the parenthesis then I distributed the exponent.
= 64

(5+3)^2
=5^2+3^2
=25+9
=34
• what does he mean when he says( 7x*10)*2?
• Are you using * as a multiplication sign?
• find the product (s-1)(s+1)
• Two options here: Either you know your rules for binomials and write down (s^2-1) or you use the distributive property twice:
``(s-1)(s+1)= s(s+1) - 1(s+1)= s^2 + s - s - 1= s^2 - 1``
• how do I do (x^2)^2? Is it x^5? Do we add the exponents or multiply them?
• Sooo, 900x+900x would equal 1,800x. Am I right?
• need to know the differnce of squares
• Any time a binomial has 2 terms which are perfect squares subtracted from each other, it is a difference of squares, and it factors like this:
`a^2 - b^2 = (a+b)(a-b)`

Examples:
x^2 - 4 = (x+2)(x-2)
a^2 - 16 = (a+4)(a-4)
4y^2 - 9q^2 = (2y + 3q)(2y - 3q)
25x^2 - 1 = (5x+1)(5x-1)
• how did he distribute it to that long expression?
(1 vote)
• Okay, so!

(7x+10)^2

You have (7x+10) BUT You have the exponent of 2, so that means you're multiplying, when multiplying polynomials you must simplify like regular multiplication

Which is multiplying it by itself because it's squared

Meaning you are left with (7x+10) times (7x+10)

So you take the 7x out of the (7x+10) and multiply it by the remaining (7x+10), because when something is squared you are multiplying by itself.

Therefore 7x(7x+10) would make 49X^2 + 70x

because 7*7 is 49 but you still have the x, and X and another X is the same as X^2. Now again you multiply 7x by 10 and get 70x, because the X just doesn't disappear.

Now, you multiplied one factor with the equation, but what about the +10? So now we just multiply 10 times the same equation!

So 10(7x+10), 10*7x is 70x because you are still multiplying the X by the coefficient, so a constant times a coefficient does nothing to the variable. Now you multiply 10 times 10 to get 100, leaving you with 70x+100

Now, you are left with 49x^2+70x+70x+100, just combine like terms, which would be 70x and 70x because they are both real numbers and share the variable X, Leaving you with 49x^2 + 140x + 100

I hope this helps you, it gets easier when you practice. send me a message if you need anymore help.
• (a+b)^3 , I wanna know how to do this step by step. I dont know why they answer is the way it is. Not just the answer but how to do step by step?
(1 vote)
• (a+b)^3
= (a+b)(a+b)(a+b)
Use FOIL rule to multiply the last 2 binomials. Do you know FOIL?
= (a+b)(a^2 + 2ab + b^2)
= a(a^2 + 2ab + b^2) + b(a^2 + 2ab + b^2)
= (a^3 + 2a^2b + ab^2) + (a^2b + 2ab^2 + b^3)
= a^3 + 2a^2b + a^2b + ab^2 + 2ab^2 + b^3
= a^3 + 3a^2b + 3ab^2 + b^3
• So I was solving problems in the "Multiplying Binomials by Binomials Practice" and I came across this one problem that I didn't understand.
The problem was as follows:
`` (x - 7)(x - 5) = x^2 - 12x + d``

I simplified the equation to:
``x^2 - 5x - 7x + 35``

But I don't understand how 5x - 7x = 12x. Shouldn't 5x - 7x be something like -2x?
(1 vote)
• Oh you didn't look at the equation correctly! It's actually supposed to be -5x - 7x, always take the negative sign in front of it. And it's supposed to be -12x not 12x. So -5x - 7x = -12x.
Hope this helped :D

Pssstt...by the way, I love the username!!