Remember to factor out the GCF of the coefficients if there is one. A perfect square binomial will always follow the pattern a squared plus or minus 2ab plus b squared. If it's plus 2ab, that factors to (a + b)(a + b) If it's minus 2ab, that factors to (a - b)(a - b)
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.
Two possibilities here. 9x - 30x +25 = -21x + 25 and done, but I don't think you mean that. 9x² - 30x + 25 is more likely. This is easier than normal, since this follows the square pattern. (ax-b)² = a²x²-2ab+b² a² = 9 so a=3 b² = 25 so b=5 3*5*2 = 30, so it checks. (3x-5)(3x-5) = 9x² -15x - 15x + 25 = 9x² -30x + 25 ■
2ab
Yes.
a^2 + b^2 + 2ab = (a + b)^2
a square plus 2ab plus b square
(A+B)2 = (A+B).(A+B) =A2+AB+BA+B2 =A2+2AB+ B2 So the Answer is A + B the whole square is equal to A square plus 2AB plus B square. Avinash.
Remember to factor out the GCF of the coefficients if there is one. A perfect square binomial will always follow the pattern a squared plus or minus 2ab plus b squared. If it's plus 2ab, that factors to (a + b)(a + b) If it's minus 2ab, that factors to (a - b)(a - b)
It is a trinomial.The square of (a + b)^2 is a^2 + 2ab + b^2.
(a-b)2 = a2 _ 2ab+b2
It is a trinomial.The square of (a + b)^2 is a^2 + 2ab + b^2.
(a - b)2 = a2 - 2ab + b2 square ft
k can be 2 or -2. A binomial squared is: (a + b)² = a² + 2ab + b² Given x² - 5kx + 25 = (a + b)² = a² + 2ab + b² we find: a² = x² → a = ±x 2ab = -5kx b² = 25 → b = ±5 If we let a = x, then: 2ab = 2xb = -5kx → 2 × ±5 = -5k → k = ±2 If k = 2 then the binomial is (x - 5)² If k = -2 then the binomial is (x + 5)² To be complete if a = -x, then: If k = 2 then the binomial is (-x + 5)² If k = -2 then the binomial is (-x - 5)² which are the negatives of the binomials being squared.
consider: (A+B) x (A + B) = A(A+B) + B(A+B) = A^2 + AB + BA + B^2 = A^2 + 2AB + B^2 (A-B) x (A-B) = A(A-B) - B(A-B) =A^2-AB-BA+B^2 = A^2 - 2AB + B^2 The answers are similar however square of sum has positive component and square of difference has negative component.
2ab = 2*(-2)*7 = -28
(a+b+c)²=a²+b²+c²+ 2ab+2bc+2ac