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 Pascal's Triangle to expand (4+2y)^(3). Express your answer in simplest form. Answer:

Use Pascal's Triangle to expand (4+2y)3 (4+2 y)^{3} . Express your answer in simplest form.\newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Pascal's triangle and the Binomial Theoremright chevron icon

Full solution

Q. Use Pascal's Triangle to expand (4+2y)3 (4+2 y)^{3} . Express your answer in simplest form.\newlineAnswer:
  1. Identify Exponent 33: Identify the row of Pascal's Triangle that corresponds to the exponent 33. The third row of Pascal's Triangle (starting with row 00) is 1,3,3,11, 3, 3, 1. These numbers will be the coefficients in the expanded form.
  2. Write Binomial Theorem Terms: Write out the terms using the binomial theorem and the coefficients from Pascal's Triangle.\newlineThe binomial theorem states that (a+b)n=∑k=0n(nk)⋅an−k⋅bk(a+b)^n = \sum_{k=0}^{n} \binom{n}{k} \cdot a^{n-k} \cdot b^k. For (4+2y)3(4+2y)^3, the terms will be:\newline1⋅(4)3⋅(2y)0+3⋅(4)2⋅(2y)1+3⋅(4)1⋅(2y)2+1⋅(4)0⋅(2y)31\cdot(4)^3\cdot(2y)^0 + 3\cdot(4)^2\cdot(2y)^1 + 3\cdot(4)^1\cdot(2y)^2 + 1\cdot(4)^0\cdot(2y)^3
  3. Calculate Each Term: Calculate each term separately.\newline1×(4)3×(2y)0=1×64×1=641\times(4)^3\times(2y)^0 = 1\times64\times1 = 64\newline3×(4)2×(2y)1=3×16×2y=96y3\times(4)^2\times(2y)^1 = 3\times16\times2y = 96y\newline3×(4)1×(2y)2=3×4×(2y)2=3×4×4y2=48y23\times(4)^1\times(2y)^2 = 3\times4\times(2y)^2 = 3\times4\times4y^2 = 48y^2\newline1×(4)0×(2y)3=1×1×(2y)3=8y31\times(4)^0\times(2y)^3 = 1\times1\times(2y)^3 = 8y^3
  4. Combine Terms: Combine all the terms to get the expanded form. 64+96y+48y2+8y364 + 96y + 48y^2 + 8y^3

More problems from Pascal's triangle and the Binomial Theorem

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

Posted 5 months ago

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

Posted 5 months ago

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

Posted 5 months ago

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

Posted 5 months ago

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

Posted 5 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 5 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 9 months ago

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

Posted 9 months ago

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

Posted 9 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 9 months ago

View all (43)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant