what is (x+2)(x+2) or (x+2) squared?

Question

i really don't understand the concept i know the formula is (a+b)squared = A squared+2AB+B squared

but i am still having trouble with numbers or expressions like (2x+5) squared

Answer 1

I say focus on FOIL instead of focusing on trying to remember the whole A^2 + 2AB + B^2

Let's use FOIL (First Outside Inside Last) to do the 2x+5 then let's look at how it applies to the A^2 + 2AB + b^2

(2x+5)(2x+5)

F means to multiply the first term in each bracket first:
2x * 2x=4x^2

Then you multiply the first term to the Outside term of the last bracket:

2x * 5=10x

Then you multiply the Inside terms together (the last term of the first bracket and the first term of the second bracket):

5 * 2x = 10x (do you see where the 2 AB is coming?)

Then multiply your two Last terms for each bracket:
5 * 5=25

So, (2x+5)(2x+5) gives us:

4x^2 +10x+10x+25
= 4x^2 + 20x + 25

Now, in terms of A^2 + 2AB + B, let's look at the terms individually:

a=2x, right?
b=5, right?

a^2 is therefore (2x)^2, which means (2x)(2x)= 4x^2
2ab is 2(2x)(5)=2(10x)= 20x
b^2 is 5*5=25.

Now, I don't know if you were trying to apply the a^2 + 2ab + b^2 in the same mental way that you can with the (x+2) or not. If you were, you can do it, you just have to be careful of squaring the coefficient (the 2 in the 2x) and not just the x and make sure to do the other mental math. It doesn't really work quite as well when you have a coefficient, but it can be done.

Answer 2

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

Then you multiply them with each other, we'll have:

a^2 + (a . b) + (b . a) + b^2

which equals to a^2 + ab + ab + b^2 (according to : a . b = b . a)

and we have : a^2 + 2ab + b^2

==> (a + b)^2 = (a + b) (a + b) = a^2 + 2ab + b^2

Apply the formula into the equation : (x + 2)^2

we have a = x and b = 2

(a + b)^2 = a^2 + 2ab + b^2

=> (x + 2)^2 = x^2 + 2 ( 2 . x ) + 2^2 = x^2 + 4x + 4


Another equation : (2x + 5)^2

we have a = 2x and b = 5

(a + b)^2 = a^2 + 2ab + b^2

=> (2x)^2 + 2 ( 2x . 5) + 5^2 = 4x^2 + 20x + 25.

Answer 3

the formula is just for user to remember the final version easily.
The ( a + b ) ^ 2 = ( a + b ) ( a + b ) right?
= a ( a + b ) + b ( a + b ) right?
= a^2 + ab + ab + b^2 right?
= a squared + 2ab + b squared

got it?
so ( 2x + 5 ) = ( 2x ) ^2 + 2*2x*5 + 5 ^2 = 4x^2 + 20x + 25
if you just learnt this formula recently, you can deal questions step by step. after several days experices, you will be familiar with the formula.

Answer 4

I was just going to answer it but i guess i could explain it.

The most important thing to remember is to use the foil method.
FOIL(first, outer, inner, last)

For the problem (x+2)(x+2) you multi. using FOIL. The First two you multi are x times x. This will give you x^2. Then you multi the terms on the Outside: x times 2, this will give you 2x. Next you multi the Inner terms: 2 times x, this will give you the same answer as before 2x. Finally, you multi the Last two terms: 2 times 2, this will give you 4. Then you write down each product.

x^2+2x+2x+4, but because we add like terms(2x) we can rewrite this as:

x^2+4x+4.

As for the (2x+5)^2, you do the same thing.

The First two you multi are 2x times 2x. This will give you 4x^2. Then you multi the terms on the Outside: 2x times 5, this will give you 10x. Next you multi the Inner terms: 5 times 2x, this will give you the same answer as before 10x. Finally, you multi the Last two terms: 5 times 5, this will give you 25. Then you write down each product.

4x^2+10x+10x+25, Adding like terms gives you:

4x^2+20x+25

It is very important to remember the rule of signs when multiplying, or you would get the wrong numbers. In both the problems you have all the numbers are positive so you didn't have to worry about it when adding like terms.

Hoped this helped.

Answer 5

well both are the same thing, first lets use (x+2)(x+2), first multiply x times x, that will give you x squared, then x times two, wich will give you 2x, and then move to the 2, multiply 2 times x, again you will get 2x, and then 2 times 2, which equals 4, at the end you will get xsquared (I dont know how to type the squared sign) so it is xsquared +2x+2x+4, combine the 2x's, and your final answer is 2squared+4x+4, after that you cant do anything else!! you're done!!

Answer 6

see it's very easy
take A = x
and B = 2
now u know that (A+B)squared is Asquared + 2AB + Bsquared
so (x+2)squared = x-square +2(x)(2) + 2-square
= xsquare +4x + 4

and for (2x+5)square do the same

Answer 7

The answer to your initial question is:

X squared + 4x + 4
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To help out with the other expression you gave:

(2x + 5) squared is the same as (2x + 5)(2x + 5)
To solve that, multiply each value in the first parentheses to both values in the second parentheses.

In other words, start with the first 2x. Multiply that by both values in the second parentheses (2x and 5)

So, 2x times 2x and 2x times 5
This results in 4x squared and 10x

So now you have 2x squared + 10x.

Now, multiply the second value in the first parentheses by both values in the second parentheses.

To do this, start with the first 5. Multiply it by 2x and 5.
This gives you 10x and 25.

Combine the first step with the second and you have:
4x squared + 10x + 10x + 25

This can be simplified to 4x squared + 20x + 25.
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So to express what I just explained in variables:

Let's say you have (a+b)(c+d)
First, multiply a by the terms in the second parentheses:

a x c and a x d

this gives you ac + ad

Next, multiply b by both terms in the second parentheses:

b x c and b x d

This gives you bc + bd

Combine them to form ac + ad + bc + bd. That is the answer.
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It is easier to square the same expression, so you have:

(a+b)(a+b)

Using the steps from the explanations above and simplifying, the answer to any question like (a+b)(a+b) will ALWAYS be:

a squared + ab + ab + b squared
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Hope you understand the concept now =)

Answer 8

See,there are 2 methods to do this problem
1. write (x+2) (x+2)=
x(x+2)+2(x+2)
xsquared+2x+2x+4
=xsquared+4x+4
2. Or use the identity=Asquared+2AB+Bsquared
xsquare+2xXx2+2square=
xsquare+4x+4

Answer 9

think of the A and the B to have an exponets of one.
(a+b)squared=
a to the first power plus 2 times a to the first and b to the first plus b to the first.

NOw you add all of the like terms' exponents leaving you with A squared plus B Squared or (a+b) squared because the 2 exponent is distributed within the parenthesis

Answer 10

x^2+4x+4

The method we always learned in school was called the FOIL method. It stands for Front Outer Inner Last.
Front = x*x
+
Outer = x*2
+
Inner = 2*x
+
Last = 2*2

Thus the total = x^2 + 2x +2x + 4
= x^2 +4x + 4