Warm Up 03.31.25 Binomial expansion BK01

Which row of Pascal's Triangle is used to expand (x + y)³?

• 1 2 3 4

• 1 3 3 1

• 1 4 6 4

• 1 5 10 10

What is the expansion of (2x + 3)²?

• 4x² + 12x + 8

• 4x² + 12x + 9

• 4x² + 6x + 9

• 2x² + 6x + 9

What is the expansion of (x - 1)⁴?

• x⁴ - 4x³ + 6x² - 4x + 1

• x⁴ - 3x³ + 3x² - 1

• x⁴ - 5x³ + 10x² - 5

• x⁴ - 2x³ + 4x² - 2

What is the relationship between the number of terms in the expansion of (a + b)ⁿ and n?

• The number of terms is n + 1.

• The number of terms is n.

• The number of terms is 2n.

• The number of terms is n - 1.

How many terms are in the expansion of (1 + b)⁵?

• 4

• 5

• 6

• 7

What is the expansion of (x − y)³?

• x³ − 3x²y + 3xy² − y³

• x³ + 3x²y + 3xy² + y³

• x³ − 3x²y − 3xy² + y³

• x³ − 3x²y + 3xy² + y³

What is the expansion of (x + 2y)⁴?

• x⁴ + 8x³y + 24x²y² + 32xy³ + 16y⁴

• x⁴ + 4x³y + 6x²y² + 8xy³ + 2y⁴

• x⁴ + 16x³y + 24x²y² + 32xy³ + 8y⁴

• x⁴ + 12x³y + 36x²y² + 48xy³ + 24y⁴

What is the general term in the binomial expansion of (a + b)ⁿ?

• T(k+1) = C(n, k) * a^(n-k) * b^k, where C(n, k) is the binomial coefficient.

• T(k) = C(n, k) * a^(k) * b^(n-k), where C(n, k) is the binomial coefficient.

• T(k) = C(n, k) * a^(n+k) * b^(n-k), where C(n, k) is the binomial coefficient.

• T(k+1) = C(n, k) * a^(k) * b^(k), where C(n, k) is the binomial coefficient.

What is the Binomial expansion of (x + 1)⁵?

• x⁵ + 5x⁴ + 10x³ + 10x² + 5x + 1

• x⁵ + 4x⁴ + 6x³ + 4x² + 1

• x⁵ + 6x⁴ + 15x³ + 20x² + 15x + 6

• x⁵ + 5x⁴ + 6x³ + 4x² + 1

What is the significance of Pascal's Triangle in binomial expansion?

• It provides the coefficients for the terms in the expansion.

• It calculates the roots of polynomial equations.

• It determines the convergence of infinite series.

• It represents the Fibonacci sequence.