(a + 2b)(c + 2d)
(2a + b)(2c + d)
(a - 2b)(c - 3d)
a^2 + b^2 + c^2 - ab - bc - ca = 0=> 2a^2 + 2b^2 + 2c^2 - 2ab - 2bc - 2ca = 0 => a^2 - 2ab + b^2 + b^2 - 2bc + c^2 + c^2 - 2ca + a^2 = 0 => (a - b)^2 + (b - c)^2 + (c - a)^2 = 0 Each term on the left hand side is a square and so it is non-negative. Since their sum is zero, each term must be zero. Therefore: a - b = 0 => a = b b - c = 0 => b = c.
(2a + b)(2c + d).
ac + 2ad + 2bc + 4bd = a(c + 2d) + 2b(c + 2d) = (a + 2b)(c + 2d) Now expand to confirm your answer: c(a + 2b) + 2d(a + 2b) = ac + 2bc + 2ad + 4bd ≡ ac + 2ad + 2bc + 4bd
4ac + 2ad + 2bc +bd = 2a*(2c + d) + b*(2c + d) = (2c + d)*(2a + b)
(2a + b)(2c + d)
(2a + b)(2c + d)
(2a + b)(2c + d)
ac + 2ad + 2bc + 4bd (ac + 2ad) + (2bc + 4bd) group the figures a(c + 2d) + 2b(c + 2d) remove the common divisors of each set (a + 2b)(c + 2d) take the figures in parentheses as one set, and add the outside figures as the other
(a - 2b)(c - 3d)
ab-2ac+b^2-2bc
a2+2ab+b2+2ac+2bc+c2+2ad+2ae+2bd+2be+2cd+2ce+d2+2de+e2
(a + b)(b - 2c)
(a + b)(b - 2c)