a2b2 - 2ab - 25 is a quadratic expression in the variables ab. There is no equation or inequality in the question so there is nothing that can be solved.
Because of the nature of the expression a and b cannot be separated in any meaningful way.
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.
The square of a sum, expressed as ((a + b)^2), expands to (a^2 + 2ab + b^2). In contrast, the square of a difference, represented as ((a - b)^2), expands to (a^2 - 2ab + b^2). The key difference lies in the sign of the middle term: the square of the sum includes a positive (2ab), while the square of the difference includes a negative (2ab). This distinction affects the overall value of the expressions when (a) and (b) are not equal.
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
False. A perfect square trinomial takes the form ( (a - b)^2 = a^2 - 2ab + b^2 ) or ( (a + b)^2 = a^2 + 2ab + b^2 ). The expression ( 16x^2 - 36x + 9 ) can be factored as ( (4x - 3)^2 ), which confirms it is a perfect square trinomial, but it does not fit the specified form ( a^2 - 2ab b^2 ).
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.