Write the number of terms in the expansion of (x+a)^6
X^6 .......+ _X^1 + a^6
That is 7
Ah, the expansion of (x+a)^6! It's like watching a fascinating firework show, but with algebraic terms bursting into the mathematical sky. So, let's count those terms, shall we?
The binomial theorem comes to our rescue here. According to this theorem, the number of terms in the expansion of (x+a)^n is given by (n+1). So, for (x+a)^6, we can expect a grand total of 6+1 = 7 terms.
Why 7, you might ask? Well, n represents the power of the binomial, which in this case is 6. And hey, adding 1 for good measure never hurt anyone!
So there you have it, 7 terms will light up the sky in the expansion of (x+a)^6. Enjoy the mathematical fireworks!
To find the number of terms in the expansion of (x+a)^6, you can use the binomial theorem. According to the theorem, the number of terms in the expansion of (x+a)^n can be found by adding 1 to the exponent and considering it as the number of terms in the expression.
In this case, the exponent is 6, so the number of terms is given by:
Number of terms = 6 + 1 = 7
Therefore, the expansion of (x+a)^6 will have 7 terms.
To find the number of terms in the expansion of (x+a)^6, we can use the binomial theorem.
The binomial theorem states that for any expression (x + a)^n, the number of terms in the expansion is equal to (n + 1).
In this case, (x + a)^6, the number of terms in the expansion will be (6 + 1) = 7.
Therefore, the number of terms in the expansion of (x + a)^6 is 7.