4aa-bb fits the special type of polynomial in the form of x**2-y**2 which can be rewritten as (x-y)(x+y)
sqrt(4aa) = 2a
sqrt(bb) = b
(2a-b)(2a+b)
There is a formula for the difference of squares. In this case, the answer is (C + D)(C - D)
(x - 7)(x2 + 7x + 49)
4r - 25 does not factor. If that were 4r2 - 25, it would be the difference of two squares, which factors to (2r - 5)(2r + 5)
If a polynomial has factors x-6 and x-3 it will equal 0 if either factor equals 0 since the other factor then would be multiplied by 0. ie. 0 * (x-6)=0 and 0 * (x-3)=0. so x=3 or 6
With great difficulty not knowing if 6x and 27 are plus or minus
6n(2n - 3)
The factors are -1(2x + 1)(3x + 4)
(2x - 4)(2x + 3) The key is to look for all the factor pairs of 12.
(8w + 7)(8w - 7)
Depending on the missing operational sign, that would be 2(x plus or minus 8)
(x squared plus the square root of 2) times (x squared minus the square root of 2).
n(2n - 1)(2n + 7)
( x - y )2There isn't enough information to answer this question because they have two squared variables and you do not know what is being squared. You would first need to either know the value of one of the variables and an equation of the value of both of the variables before you would be able to factor.
(a+b)(a-b)
I suppose that would be 14x2 - 7x3. Just take out the common factor, 7x2. Divide each term by this factor to find the other factor.
The discriminant of this quadratic expression is less than zero therefore it cannot be factored.
You can factor this multivariate polynomial (a polynomial with several variables, here x and y), by looking at it as a univariate polynomial in either x or y. This would give you a simple second order equation of the form ax2+bx+c, which you can solve. This will give you 2 solutions, say x1 and x2, and can then factor your polynomial to a(x-x1)(x-x2). In our case: a=8, b=-y and c=-7y2 and the solutions for this equation are x1=y and x2=-7/8*y and this gives us 8x2 - xy -7y2 = 8(x-y)(x+7/8y) = (x-y)(8x+7y)