Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Use Pascal's Triangle to expand
(2-5y)^(4). Express your answer in simplest form.
Answer:

Use Pascal's Triangle to expand $(2-5 y)^{4}$ . Express your answer in simplest form. $\newline$ Answer:

View step-by-step help

View step-by-step help

Pascal's triangle and the Binomial Theorem

Full solution

Q. Use Pascal's Triangle to expand

(2-5 y)^{4}

. Express your answer in simplest form.

\newline

Answer:

Identify Row: Identify the row of Pascal's Triangle that corresponds to the exponent $4$ . The row for the exponent $4$ is the fifth row (starting with row $0$ for the exponent $0$ ), which is $1, 4, 6, 4, 1$ .
Write Terms: Write out the terms using the binomial coefficients from Pascal's Triangle. $\newline$ The terms will be: $\newline$ $1\times(2)^4\times(-5y)^0 + 4\times(2)^3\times(-5y)^1 + 6\times(2)^2\times(-5y)^2 + 4\times(2)^1\times(-5y)^3 + 1\times(2)^0\times(-5y)^4$
Simplify Terms: Simplify each term. $\newline$ $1\times(16)\times1 + 4\times(8)\times(-5y) + 6\times(4)\times(-5y)^2 + 4\times(2)\times(-5y)^3 + 1\times1\times(-5y)^4 = 16 - 160y + 6\times4\times25y^2 - 8\times125y^3 + 625y^4$
Perform Multiplications: Continue simplifying by performing the multiplications. $\newline$ $= 16 - 160y + 600y^2 - 1000y^3 + 625y^4$
Final Expression: Write the final expression in standard polynomial form, with the terms in descending order of the exponent. $\newline$ $= 625y^4 - 1000y^3 + 600y^2 - 160y + 16$

More problems from Pascal's triangle and the Binomial Theorem

Question

Find the degree of this polynomial.

\newline

`5b^{10} + 3b^3`

\newline

Posted 2 months ago

Question

\newline

(9a + 5) - (2a + 4)

\newline

Posted 2 months ago

Question

Find the product. Simplify your answer.

\newline

-3v^2(v^2 - 9)

\newline

Posted 1 month ago

Question

Find the product. Simplify your answer.

\newline

(v - 3)(4v + 1)

\newline

Posted 2 months ago

Question

Find the square. Simplify your answer.

\newline

(3y + 2)^2

\newline

Posted 2 months ago

Question

Divide. If there is a remainder, include it as a simplified fraction.

\newline

(24t^2 + 36t) \div 6t

\newline

Posted 2 months ago

Question

Is the function

q(x) = x^6 - 9

even, odd, or neither?

\newline

\newline

\text{[[even][odd][neither]]}

Posted 2 months ago

Question

Find the product. Simplify your answer.

\newline

-3q^2(-3q^2 + q)

\newline

Posted 2 months ago

Question

Find the product. Simplify your answer.

\newline

(r + 3)(4r + 2)

\newline

Posted 2 months ago

Question

Find the roots of the factored polynomial.

\newline

(x + 7)(x + 4)

\newline

Write your answer as a list of values separated by commas.

\newline

x =

Posted 2 months ago