To expand the binomial (d - 3)^6 using Pascal's Triangle, we can follow these steps:
1. Write down the sixth row of Pascal's Triangle.
The sixth row of Pascal's Triangle is: 1 5 10 10 5 1
2. Split the binomial into two terms: d^6 and -3^6.
3. Starting with the first term, use the row of Pascal's Triangle to determine the coefficients for each term.
Term 1: d^6 * 1 = d^6
Term 2: d^5 * (-3) * 5 = -15d^5
Term 3: d^4 * (-3)^2 * 10 = 90d^4
Term 4: d^3 * (-3)^3 * 10 = -270d^3
Term 5: d^2 * (-3)^4 * 5 = 405d^2
Term 6: d * (-3)^5 * 1 = -243d
Term 7: (-3)^6 * 1 = 729
4. Combine all the terms:
(d - 3)^6 = d^6 - 15d^5 + 90d^4 - 270d^3 + 405d^2 - 243d + 729
Use Pascal's Triangle to expand the binomial. (d – 3)6 (1 point)
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