Simplify the following expression: (2a + 3b + 4c)2 + (2a − 3b − 4c)2 − 8a2 − 18b2 −32c2
48bc
Put X = 2a and Y = 3b + 4c, so the first two terms are (X + Y)2 + (X − Y)2 = 2X2 + 2Y2.
2X2 = 8a2, and 2Y2 = 2(9b2 + 24bc + 16c2) = 18b2 + 48bc + 32c2.
So the first two terms give 8a2 + 18b2 + 32c2 + 48bc; subtracting 8a2, 18b2 and 32c2 leaves 48bc.
Hence, the answer is 48bc.
Similar Questions
If \(x + \dfrac{1}{x} = 17\), then the value of \(x^2 + \dfrac{1}{x^2}\) is:
What is the value of (x + 2)2 − (x − 2)2 when x = 1?
If a + b = 9 and ab = 13, then the value of a³ + b³ is:
If a + b = 9 and ab = 13, then the value of \((a^2 + b^2)(a^3 + b^3)\) is:
Expand \((a - p + m)^{2}\).
If \(49a^{2} - b = \left(7a + \dfrac{1}{2}\right)\left(7a - \dfrac{1}{2}\right)\), then the value of b is:
Simplify: \((2a + 3b)^2 - (2a - 3b)^2\)
Simplify: (2x + 3y)(2x − 3y)
Simplify: \((3\sqrt{5} + 2\sqrt{3})^{2} - (3\sqrt{5} - 2\sqrt{3})^{2}\).
If \(x + \dfrac{1}{x} = \sqrt{20}\), find the value of \(x^{3} - \dfrac{1}{x^{3}}\), where \(x > 1\).
Important Questions from Identities
If \(2x + { {1} \over 3x}= 5, x ≠ 0\) , then what is the value of \(27x^3+{{1} \over 8x^3}\) ?
If x 2 + 4y 2 = 40, xy = 6 and x > 2y then the value of x - 2y is:
- \(\dfrac{(5.17-2.19)^2-(5.17+2.19)^2}{11.3223}\)
If a(a + b + c) 2= 1792; b(a + b + c) 2= 1536; c(a + b + c) 2= 768 then what will be the value of a?
If a + b + c = 5, a 2+ b 2+ c 2= 27, a 3 + b 3 + c 3 = 125, then the value of \(\frac{abc}{5}\) is:
