Answer:
Term coefficient
Explanation:
You can use Pascal's triangle to predict the coefficient of each term in a binomial expansion.
Since the binomial has exponent 7, the expanded expression will have 8 terms: (x + y)⁰ has 1 term, (x + y)¹ has two terms, (x + y)² has three terms, (x + y)³ has four terms, and so on.
The Pascal triangle for 8 terms has 8 rows and they are:
1 row 1
1 1 row 2
1 2 1 row 3
1 3 3 1 row 4
1 4 6 4 1 row 5
1 5 10 10 5 1 row 6
1 6 15 20 15 6 1 row 7
1 7 21 35 35 21 7 1 row 8
So, the coefficients, in order, are the numbers from the row 8: 1, 7, 21, 35, 35, 21, 7, and 1.
And the terms in order are: x⁷y⁰, x⁶y¹, x⁵y², x⁴y³, x³y⁴, x²y⁵, x¹y⁶, and x⁰y⁷.
With that, you can write the coefficient of each term:
Term coefficient
x⁷y⁰ = x⁷ 1
x⁶y¹ = x⁶y 7
x⁵y² 21
x⁴y³ 35
x³y⁴ 35
x²y⁵ 21
x¹y⁶ = xy⁶ 7
x⁰y⁷ = y⁷ 1
