How do i factor this36(2x-y)^2-25(u-2y)^2

  • Thread starter dcgirl16
  • Start date
In summary, to factor the expression 36(2x-y)^2-25(u-2y)^2, we can use the difference of two squares formula to get (6(2x-y))^2-(5(u-2y))^2. From there, we can simplify the coefficients outside the brackets and use substitution to make the factoring process easier.
  • #1
dcgirl16
27
0
how do i factor this
36(2x-y)^2-25(u-2y)^2

i was thinking to expand the brackets first?? but I am not really sure
 
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  • #2
In general the difference of two squares (which is what you have) is easily factored.

a^2-b^2=(a+b)(a-b)
 
  • #3
alright so once I've got that what do i do with the 25 and 36 outside the brackets
 
  • #4
Once you 'do that' you don't have any 25 or 36 outside any brackets.
 
  • #5
5^2 = 25
6^2 = 36
 
  • #6
Let 2x-y=A and u=2y=B

36(A^2) - 25(B^2)= (6A)^2 - (5B)^2
 
  • #7
Since we know 6^2 = 36 could you do it easier if it was written as: 36(2x-y)^2 = 6^2(2x-y)^2 = [(6)(2x-y)]^2 and you did the same process to simplify the other term.
 

1. How do I factor a quadratic expression?

To factor a quadratic expression, you need to find two numbers that multiply to the first term and add to the second term. In this case, the first term is 36 and the second term is -25. Therefore, the factors of 36 that add up to -25 are -9 and -4.

2. What is the difference of squares?

The difference of squares is a special case of factoring a quadratic expression where the expression is in the form of a2 - b2. In this case, the expression is 36(2x-y)^2-25(u-2y)^2, which can be rewritten as (6(2x-y))^2 - (5(u-2y))^2. This is a difference of squares because the first term is squared and the second term is squared with a negative sign.

3. How do I factor a difference of squares?

To factor a difference of squares, you can use the formula a2 - b2 = (a+b)(a-b). Applying this to the expression (6(2x-y))^2 - (5(u-2y))^2, we get (6(2x-y) + 5(u-2y))(6(2x-y) - 5(u-2y)). This is the factored form of the expression.

4. Why do we need to factor expressions?

Factoring expressions helps simplify them and make them easier to work with. It also allows us to solve equations and find the roots of a quadratic function. In some cases, factoring can also help us identify special patterns or relationships within the expression.

5. Can I use the quadratic formula to solve this expression?

No, the quadratic formula is used to solve quadratic equations, not to factor expressions. However, you can use the quadratic formula to find the roots of the quadratic expression after it has been factored.

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