Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Use the Binomial Theorem to complete the expansion of (x+2)4(x + 2)^4.x4+8x3+24x2+32x+‾x^4 + 8x^3 + 24x^2 + 32x + \underline{\hspace{1cm}}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Binomial Theorem IIright chevron icon

Full solution

Q. Use the Binomial Theorem to complete the expansion of (x+2)4(x + 2)^4.x4+8x3+24x2+32x+‾x^4 + 8x^3 + 24x^2 + 32x + \underline{\hspace{1cm}}
  1. Identify general term: Identify the general term in the binomial expansion: T(k+1)=C(n,k)⋅a(n−k)⋅bkT(k+1) = C(n, k) \cdot a^{(n-k)} \cdot b^k where n=4n=4, a=xa=x, and b=2b=2.
  2. Calculate missing term: Calculate the missing term, which is the constant term when k=4k=4: T(5)=C(4,4)⋅x(4−4)⋅24T(5) = C(4, 4) \cdot x^{(4-4)} \cdot 2^4.
  3. Perform calculations: Perform the calculations: C(4,4)=1C(4, 4) = 1, x0=1x^0 = 1, and 24=162^4 = 16. So, T(5)=1×1×16=16T(5) = 1 \times 1 \times 16 = 16.

More problems from Binomial Theorem II

Question
Find the degree of this polynomial.\newline`5b^{10} + 3b^3`\newline_______
Get tutor helpright-arrow

Posted 2 months ago

Question
Subtract.\newline(9a+5)−(2a+4)(9a + 5) - (2a + 4)\newline____
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the product. Simplify your answer. \newline−3v2(v2−9)-3v^2(v^2 - 9)\newline________
Get tutor helpright-arrow

Posted 1 month ago

Question
Find the product. Simplify your answer.\newline(v−3)(4v+1)(v - 3)(4v + 1)\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the square. Simplify your answer.\newline(3y+2)2(3y + 2)^2\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Divide. If there is a remainder, include it as a simplified fraction.\newline(24t2+36t)÷6t(24t^2 + 36t) \div 6t\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Is the function q(x)=x6−9 q(x) = x^6 - 9 even, odd, or neither?\newlineChoices:\newline[[even][odd][neither]]\text{[[even][odd][neither]]}
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the product. Simplify your answer. \newline−3q2(−3q2+q)-3q^2(-3q^2 + q)\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the product. Simplify your answer.\newline(r+3)(4r+2)(r + 3)(4r + 2)\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the roots of the factored polynomial.\newline(x+7)(x+4)(x + 7)(x + 4)\newlineWrite your answer as a list of values separated by commas.\newlinex=x = ____
Get tutor helpright-arrow

Posted 2 months ago

View all (3)