Factorise the expressions
9y^2-25
x^2-x-12
I'm totally stuck!
The first is a difference of two squares.
(3x-5)(3x+5)
The second is
(x-4)(x+3) anytime the last term is negative, you have factors with different signs
To factorize the expressions, we can use the factoring techniques.
For the expression 9y^2-25:
Step 1: Recognize that it is in the form of a difference of squares (a^2 - b^2). In this case, a = 3y and b = 5.
Step 2: Apply the formula for the factorization of a difference of squares: (a^2 - b^2) = (a + b)(a - b).
Step 3: Substitute the values of a and b into the formula: 9y^2 - 25 = (3y + 5)(3y - 5).
Therefore, the fully factorized expression is (3y + 5)(3y - 5).
Now, let's factorize the expression x^2 - x - 12:
Step 1: Look for two numbers that multiply to give the constant term (-12) and add up to give the coefficient of the linear term (-1). In this case, the numbers are -4 and 3.
Step 2: Rewrite the middle term (-x) using these two numbers: -x = -4x + 3x.
Step 3: Group the terms and factor by grouping:
x^2 - 4x + 3x - 12 = (x^2 - 4x) + (3x - 12).
Step 4: Factor out the greatest common factor from each group:
x(x - 4) + 3(x - 4).
Step 5: Notice that we have a common factor of (x - 4) in each group, so we can combine terms using this common factor.
(x - 4)(x + 3).
Therefore, the fully factorized expression is (x - 4)(x + 3).
By following these steps, you will be able to factorize similar expressions.