You can do this by finding two numbers whose product is equal to the product of the coefficients on the first and last terms, and whose sum is equal to the coefficient of the middle term. So we want two numbers, call them A and B, that add to make 3 and multiply to make -2 * 9, or -18. Those numbers would be six and negative three.
You can take those numbers and break the middle term down into two terms using them as their coefficients:
9x2 + 3x - 2
= 9x2 + 6x - 3x - 2
Now factor out like terms:
= 3x(3x + 2) - 1(3x + 2)
And group:
= (3x - 1)(3x + 2)
18x2 + 2= 2(9x2 + 1)= 2(9x2 - -1)= 2[(3x)2 - i2]= 2(3x + √-1)(3x - √-1) (substitute i for √-1)= 2(3x + i)(3x - i)
9x2...I guess that means 9x squared ? The problem: 9x(squared)+12x+4 Here's the answer: (3x+2)(3x+2) or even more simplified: (3x+2) squared
(3x)^(2-4) = (3x)^-2 = (9x2)^-1 = 1/(9x2)
9x2 + 24xy + 16y2 = 9x2 + 12xy + 12xy + 16y2 = 3x(3x + 4y) + 4y(3x + 4y) = (3x + 4y)*(3x + 4y) = (3x + 4y)2
The first equation factors to (3x + 2)(3x + 4) The second equation factors to (3a + 2b)(3a + 4b)
9x2 + 12x + 4 = 9x2 + 6x + 6x + 4 = 3x(3x + 2) + 2(3x + 2) = (3x + 2)(3x + 2) = (3x + 2)2
9x2 + 9x - 10 =(3x - 2)(3x + 5)
9x2 + 6x + 1 = 9x2 + 3x + 3x + 1 = 3x(3x + 1) + 1(3x + 1) = (3x + 1)(3x + 1) or (3x +1)2
18x2 + 2= 2(9x2 + 1)= 2(9x2 - -1)= 2[(3x)2 - i2]= 2(3x + √-1)(3x - √-1) (substitute i for √-1)= 2(3x + i)(3x - i)
One of the factors is 3x + 8b. The other is 9x^2 -24xb + 64b^2
3x(x^2 - 3x + 1)
9x^2-6xy+y^2 = (y-3x)^2 (y-3x)^2-81 -> ((y-3x)+9)((y-3x)-9)
-6x + 9x2 - 24 = 3(3x2 - 2x - 8) = 3(3x2 - 6x + 4x - 8) = 3(3x(x - 2) + 4(x - 2)) = 3(3x + 4)(x - 2)
If you mean: 9x2+3x-2 = (3x+2)(3x-1) when factored
There's a chance this was notated incorrectly. It looks like it wants to be some combination of 3x and 2. 9x2 + 12x + 4 = (3x + 2)(3x + 2) or (3x + 2)2 -9x2 - 12x - 4 = -(3x + 2)2 9x2 - 12x + 4 = (3x - 2)2 -9x2 + 12x - 4 = -(3x - 2)2
9x2...I guess that means 9x squared ? The problem: 9x(squared)+12x+4 Here's the answer: (3x+2)(3x+2) or even more simplified: (3x+2) squared
9x2 - 6xy + y2 - 81 = (3x - y)2 - 81 (since the first three terms make a perfect square = (3x - y - 9)(3x - y + 9) since the expression now is a difference of two squares.