Question

Use pascal's triangle to expand the binomial

(4x + 3y)³

Answer 1

Explanation:

l don't know how to solve

it

Answer 2

`\boxed{x^4+4x^3y+6x^2y^2+4xy^3+y^4\\}`

Explanation:

Pascal’s triangle defines the coefficients which appear in binomial expansions. That means the nth row of Pascal’s triangle comprises the coefficients of the expanded expression of the polynomial (a + b)ⁿ

To create Pascal's triangle for any n in (a + b)ⁿ ,

• To build the triangle, start with "1" at the top, then continue placing numbers below it in a triangular pattern.
  

• Each number is the numbers directly above it added together. Add the upper left and upper right diagonals to compute an entry. If a diagonal does not exist, use 0
  
• The first and last entries in each row are 1
  
• Each row of the triangle represents the coefficients of the binomial expansion of (a + b)ⁿ where n starts at 0
  

Here is Pascal's triangle for the first 5 rows. The first row is row 0

Row #

0 1

1 1 1

2 1 2 1

3 1 3 3 1

4 1 4 6 4 1

`\textrm{ Here row 0 represents $(a + b)^0$ }` =
`\boxed{\textbf{1}}`

`\textrm{Row 1 corresponds to $(a + b)^1$} =`
`\boxed{1}\;a + \boxed{1}\;b`

`\textrm{Row 2 corresponds to $(a + b)^2$} = \boxed{1}\;a^2 + \boxed{2} \;ab +\boxed{1}\;b^2`

`\textrm{Row 3 corresponds to $(a + b)^3$} = \boxed{1}\;a^3 + \boxed{3}\;a^2b + \boxed{3}\;ab^2 + \boxed{1}\;b^3`

`\textrm{Row 4 corresponds to $(a + b)^4$} = \boxed{1}\;b^4 + \boxed{4} \;a^3b +\boxed{6}\;a^2b^2 + \boxed{4} \;ab^3 + \boxed{1} \;b^4`

For the specific problem, (4x + 3y)³ use coefficients of row 3 and use 4x instead of a and 3y instead of b

`\mbox{\\ormal(4x + 3y)^3= \boxed{1}\;(4x)^3 + \boxed{3}\;(4x)^2(3y) + \boxed{3}\;4x(3y)^2 + \boxed{1}\;(3y)^3}`

`= \boxed{x^4+4x^3y+6x^2y^2+4xy^3+y^4\\} \;\;\; \textrm{ANSWER}`