Binomial Theorem Worksheets Grade 12

1. Hana is constructing a visual pattern based on the binomial expansion of (2x + 3y)^7. She arranges the terms in order of descending powers of x, forming a pyramid shape. Each term in the pyramid has a coefficient that can be found using the binomial theorem. What is the coefficient of the x^4 y^3 term in the expansion?
2. Olivia is a geneticist studying a population of 1000 plants. She knows that the probability of a single plant having a specific gene mutation is 0.15. If she randomly selects 10 plants for a detailed genetic analysis, what is the probability that exactly 3 of them will have the mutation? Use the binomial probability formula and round your answer to four decimal places.
3. Mason is designing a complex electrical circuit for a physics project. The current flowing through a specific branch of the circuit, measured in amperes, is given by the expression (2x - 5)^9, where x represents a variable resistance in ohms. Mason needs to expand this expression to analyze the circuit's behavior. Use the binomial theorem to fully expand (2x - 5)^9 and write the simplified polynomial in descending powers of x.

…and 3 more problems

1. Olivia is a financial analyst studying the growth of an investment fund. The value of the fund, in thousands of dollars, is modeled by the expression (3x + 1)^5, where x represents the number of years since the fund was established. Using the binomial theorem, expand (3x + 1)^5 completely to determine the polynomial that represents the fund's value over time.
2. Expand (4x - 3y)^8 = ?
3. Expand (5x - 3)^4 = ?

…and 5 more problems

1. Expand (2x - 7y)^4 = ?
2. Expand (5x - 4y)^6 = ?
3. Emma is an architect designing a new office building. The building's roof is shaped like a parabola and can be modeled by the function f(x) = (x - 5)^10. She needs to expand this expression to analyze the curvature coefficients for structural support. Expand (x - 5)^10 using the binomial theorem and express your answer as a simplified polynomial in descending powers of x.

…and 5 more problems