If 27(x + y) 3+ (x - y) 3= 2(2x + y) (Ax 2+ Bxy + Cy 2), then what is the value of (A - B + C)?
4
The correct answer is 4.
One powerful way to verify if an equation is an identity and to find unknown coefficients is by comparing the coefficients of like terms after expanding and simplifying both sides into a standard polynomial form. If the coefficients of each corresponding term (e.g., x^3, x^2y, xy^2, y^3, constants) on the left side match those on the right side, the equation is an identity, and the values of the unknown coefficients are determined. This method relies on the fact that a polynomial in multiple variables can be uniquely represented in a standard form.
Similar Questions
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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:
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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?
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