What are the factors of a3 b3 c3 3abc?
What are the factors of a3 b3 c3 3abc?
The value of can be easily found out to be -1 (even by simply multiplying and comparing); hence the other factor, (a2 + b2 + c2 – ab – bc – ca) . Thus a3+b3+c3−3abc = (a2 + b2 + c2 – ab – bc – ca) (a+b+c).
What is the formula of a3 b3 c3?
(a3 + b3 + c3 – 3abc) = (a + b + c)*(a2 + b2 + c2 – ab – bc – ac) 13. When a + b + c = 0, then a3 + b3 + c3 = 3abc 14.
What is a3 b3 c3 3abc?
a3 -b3 -c3− 3abc = (a -b -c)(a2 +b2 +c2 + ab – bc + ca) Hence a3 -b3 -c3 − 3abc = (a -b -c)(a2 +b2 +c2 + ab – bc + ca) 2.5 (15)
What is a³ B³ c³?
the answer will be 3abc.
What is the identity of a³ B³?
Here, volume is in cubic units. Hence, a³+b³ = (a+b) (a²-ab+b²). The algebraic identity a³+b³ = (a+b) (a²-ab+b²) has been verified.
What is the value of a3 b3 c3?
a3+b3 + c3 = 3abc.
Is a³ B³ c³ 3abc?
Answer Expert Verified a³ + b³ + c³ -3abc = ( a + b + c)(a² + b² + c² – ab – bc – ca) .
What is formula of a³ B³ c³?
How a³+b³+c³-3abc = (a+b+c )(a²+b²+c²-ab-bc-ca)
What is a³ +B³?
Difference of two squares: a² – b² = (a+ b)(a – b) Sum of two cubes: a³ + b³ = (a + b)(a² – ab + b²) Difference of two cubes: a³ – b³ = (a – b)(a² + ab + b²) Memorizing these formulas will help you solve quadratic equations quickly. …
What is the expansion of a³ B³?
Answer: Expanded form of a³-b³ = (a-b) (a²+ab+b²).
What is the value of a2 b2?
The value of a2+b2 is equal to 4 + 4 = 8. So, a2+b2 = 8.
Which is the product of a 3 + b 3-3abc?
While considering this question; quite unfortunately not from the simple perspective requested, I have found that P = a 3 + b 3 + c 3 – 3abc = 2S, where S is the area of the triangle of vertices: (a 2 – bc, c), (b 2 – ac, a), (c 2 – ab, b).
How to factor a 3 + b 3 into a factor?
Note: The factoring need not be done all the way to linear factors. All that is needed is a product of polynomials. I suggests that you use ( a + b) 3 = a 3 + b 3 + 3 a b ( a + b) ⇒ a 3 + b 3 = ( a + b) 3 − 3 a b ( a + b) instead, you will need to use it twice like this:
Can You factorise Q ( A, B, C )?
So if we regard Q Q as a polynomial in a a, then (a−b) ( a − b) will divide Q(a,b,c) Q ( a, b, c) if and only if Q(b,b,c) =0 Q ( b, b, c) = 0. Now Q(b,b,c) =b3(b−c)+b3(c−b)+c3(b−b)= 0 Q ( b, b, c) = b 3 ( b − c) + b 3 ( c − b) + c 3 ( b − b) = 0, so (a−b) ( a − b) is a factor of Q(a,b,c) Q ( a, b, c). …and hence factorise the expression completely.
How to find the factor of a-C?
Q ( a, b, c) = a 3 ( b − c) + b 3 ( c − a) + c 3 ( a − b). We can show that (a−b) ( a − b) is a factor of this expression using the Factor Theorem. This says that (x−p) ( x − p) divides the polynomial P(x) P ( x) if and only if P(p)= 0 P ( p) = 0.