(3a - 2c)(b - d)
(2a + b)(2c + d)
The GCF is 2c.
To find three odd numbers that add up to 50, we can set up an equation where x, y, and z are the three odd numbers. Since odd numbers are always in the form of 2n+1, where n is an integer, we can represent the three odd numbers as x=2a+1, y=2b+1, and z=2c+1. Therefore, the equation becomes (2a+1) + (2b+1) + (2c+1) = 50. Simplifying the equation, we get 2(a+b+c) + 3 = 50. Since 3 is odd, we cannot express it as the sum of three odd numbers.
2a + 4b + 8c = 2(a + 2b + 4c) You could also continue by factoring the inside of the parentheses a bit: 2a + 4b + 8c = 2(a + 2b + 4c) = 2(a + 2[b + 2c])
48 http://www57.wolframalpha.com/input/?i=GCD%28240+%2C+672%29
To balance the equation 4H2 + 2C, we need to adjust the number of atoms on each side of the equation. Adding a coefficient of 2 in front of C on the left side will balance the carbon atoms. The balanced equation will be 4H2 + 2C2.
You must mean, either,(1) sec2 x = sec x + 2, or(2) sec(2x) = sec x + 2.Let's first assume that you mean:sec2 x = sec x + 2;whence,if we let s = sec x, we have,s2 = s + 2,s2 - s - 2 = (s - 2)(s + 1) = 0, ands = 2 or -1; that is,sec x = 2 or -1.As, by definition,cos x = 1/sec x ,this means thatcos x = ½ or -1.Therefore, providing that the first assumption is correct,x = 60°, 180°, or 300°; or,if you prefer,x = ⅓ π, π, or 1⅔ π.Now, let's assume, instead, that you mean:sec(2x) = sec x + 2;whence,1/(cos(2x) = (1/cos x) + 2.If we let c = cos x,then we have the standard identity,2c2 - 1 = cos (2x); and,thus, it follows that1/(cos(2x) = 1/(2c2 - 1)= (1/c) + 2 = (1 + 2c)/c.This gives,1/(2c2 - 1) = (1 + 2c)/c;(2c2 - 1)(2c + 1) = 4c3 + 2c2 - 2c - 1 = c; and4c3 + 2c2 - 3c - 1 = (c + 1)(4c2 - 2c - 1) = 0.As our concern is only with real roots,c = cos x = -1; and,therefore, providing that the second assumption is correct,x = 180°; or,if you like,x = π.
-((3c - 4)(3c + 4)(2c - 5)(2c + 5))
24c2 + 96c + 90 = 6*(4c2 + 16c + 15) = 6*(2c + 3)*(2c + 5)
(b + 2c)(b - c)
4ac + 2ad + 2bc +bd = 2a*(2c + d) + b*(2c + d) = (2c + d)*(2a + b)
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(a + b)(b - 2c)
(2a + b)(2c + d)
(a + b)(b - 2c)
(3a - 2c)(b - d)