Expanding Binomial Factors

What is row 7 of Pascal's Triangle?

• 1, 5, 10, 5, 1
• 1, 5, 10, 10, 5, 1
• 1, 7, 21, 35, 35, 21, 7, 1
• 1, 7, 21, 35, 21, 7, 1

Expand (x−7)²

• x² - 14x + 49

• -x² - 14x - 49

• x² + 14x - 49

• 49x²

Select the coefficients of the 5th Row in Pascal's Triangle

• 1;3;3;1

• 1;4;6;4;1

• 1;5;10;10;5;1

• 1;6;15;20;15;6;1

Expand
(b - 2)³

• b³ - 2b² + 4b - 8
• 5b³ - 20b² + 40b - 40
• b³ - 6b² + 12b - 8
• 4b³ - 12b² + 16b - 8

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

• x⁵ + 5x⁴ + 10x³ + 10x² + 5x + 1

• x⁵ + 5x⁴ + 15x³ + 15x² + 5x + 1

• x⁵ + 6x⁴ + 15x³ + 15x² + 6x + 1

• x⁵ + 1

Expand (d-5)⁵

• d⁵ - 25 d⁴ + 250 d³ - 1250 d² + 3125 d - 3125

• d⁵ + 25 d⁴ + 250 d³ + 1250 d² + 3125 d + 3125

• d⁴ - 20d³ + 150d² - 750d + 3125

• d⁴ + 20d³ + 150d² + 750d + 3125

Evaluate responses using AI:

OFF

What would be the 5th term of the expansion of (n+4)⁴?

• 257

• 256

• n⁴

• 259

What would be the 2nd term of the expansion of (y+4)⁴?

• 253y

• 256y

• 64y

• 96y²

Analyze the expression and then choose the sentences describing whether the binomial theorem can be used to factor it. Check all that apply.

16x⁴ + 24x³ + 36x² + 54x + 81

• The value of n is 2, and the first and last terms are perfect squares

• The middle terms do not take into account the coefficients from Pascal's triangle

• The exponents on each term follow the pattern for a binomial expansion

• The expression can be factored using the binomial theorem

• The expression cannot be factored using the binomial theorem