25y2 - 49w2 = (5y)2 - (7w)2 = (5y - 7w)(5y + 7w)
175y2z
200xy2
25Y2 - 9 = 0 25Y2 = 9 Y2 = 9/25 take square root each side Y = sqrt(9/25) Y = 3/5 -----------------check 25(3/5)2 - 9 = 0 25(9/25) - 9 = 0 9 - 9 = 0 0 - 0 -------------checks
25y2 - 9 = 0Factor the expression on the left side of the equation:(5y + 3) (5y - 3) = 0The equation is a true statement if either factor is zero:5y + 3 = 05y = -3y = -3/5and5y - 3 = 05y = 3y = 3/5
I think that wants to be 16x2 - 40xy + 25y2 That factors to (4x - 5y)(4x - 5y) or (4x - 5y)2
7
You can use the formula for the difference of two squares in this case. - In general, for factoring, check whether the expression to be factored corresponds to one of several common forms - as in this case.
4x2 + 25y2 = 100 (divide each element of both sides by 100) x2/25 + y2/4 = 1 This is the equation of an ellipse of the form x2/a2 + y2/b2 = 1, whose center is at (0, 0), a = 5, b = 2, and so c = √(a2 - b2) = √19) Since the major axis is horizontal and it lies on the x-axis, the vertices are 5 units to the left and 5 units to the right of the center (0, 0). Vertices are (-5, 0) and (5, 0). The minor axis is vertical and it lies on the y-axis, so the graph of the ellipse crosses the y-axis at the points (0, -2) and (0, 2), since b = 2) The foci are √19 units to the left and √19 units to the right of the center (0, 0). The foci are (-√19, 0) and (√19, 0).
This is a special kind of expression called a difference of squares. Anything in the format a2 - b2 can be factored out as (a + b)(a - b). So we can say: x2 - 25y2 = x2 - (5y)2 = (x + 5y)(x - 5y)
(25y2 - 64) is the same thing as (5y + 8) times (5y - 8). That's only the factored form. It doesn't tell you how much the whole thing is equal to. That depends on the value of 'y', and it changes immediately any time 'y' changes.
Remember both 16 & 25 are squared numbers. 16 = 4^2 & 25 = 5^2 Hence we can write (4x)^2 - (5y)^2 Remember two squared terms with a NEGATIVE Between them will factor. ( 4x - 5y)(4x + 5y) Note the difference signs. NNB Two squared terms with a positive (+) between them DOES NOT factor.