Question

Factorise 36x^2+156xy+169y^2

Answer 1

(6x + 13y) • (6x - 13y)

Answer 2

@NetherCreep333
Please do not give direct answers. Giving direct answers will not help the asker do a similar problem, and giving direct answers will not help you check your own answer, which is exactly what you need.

Answer 3

@needdesperatehelp
When we factor an expression, here are some possible steps:
1. Common factors
Examine to see if there are factors common to ALL the terms, be they numeric (coefficients) or variables.
In this cases, there are no common factors for all three terms, so we proceed to step 2.
2. Look for standard forms
a^2+2ab+b^2=(a+b)^2...............(1)
a^2-2ab+b^2=(a-b)^2................(2)
a^2-b^2=(a+b)(a-b)....................(3)
If there are three terms, look for patterns (1) or (2).
If there are only two terms, look for pattern (3).
ALL three patters requires perfect squares at the two ends (when arranged correctly).
If this is not the case, go to step 3.
Since both 36x^2 and 169y^2 are perfect squares, we can see the expression can be expressed as
(6x)^2+156xy+(13y)^2
Then we can see that it is not case (2), nor case (3).
To confirm that this is case (1), we need to check if the middle term equals 2ab where a=6x and b=13y.
If this is the case, we have factored the expression as case (1), if not go to step 3 below.
(Check this on your own, post your result for checking if you wish).
3. Other methods.
There are other methods of factoring, including
- by inspection
- grouping,
- method of m and n
- quadratic formula
- etc.