Question

PLEASE ANSWER! I’m a tad desperate..

Select the show of Pascal’s triangle to expand the binomial expression (2x^3 + 3y^2)^7


1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

17 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1


Have a wonderful day! If you decide to answer I appreciate you very much! ❤️

Answer 1

1, 8, 28, 56, 70, 56, 28, 8, 1

Explanation:

Answer 2

1 7 21 35 35 21 7 1

Explanation:

Pascal triangle is a mathematical expression that can be used to expand questions involving bracket, especially of high degree/ power. Example:
`(a + b)^(9)` etc

For the given question, the Pascal triangle for the expansion is: 1 7 21 35 35 21 7 1

So that,

`(2x^(3)+3y^(2)) ^(7)` = 1.
`(2x^(3)) ^(7)` + 7.
`(2x^(3)) ^(6)`.
`3y^(2)` + 21.
`(2x^(3)) ^(5)`.
`(3y^(2)) ^(2)` + 35.
`(2x^(3)) ^(4)`.
`(3y^(2)) ^(3)` + 35.
`(2x^(3)) ^(3)`.
`(3y^(2)) ^(4)` + 21.
`(2x^(3)) ^(2)`.
`(3y^(2))^(5)` + 7.
`(2x^(3) )^(1)`.
`(3y^(2) )^(6)` + 1.
`(3y^(2)) ^(7)`

= 128
`x^(21)` + 1344
`x^(18)`
`y^(2)` + 6048
`x^(15)`
`y^(4)` + 15120
`x^(12)`
`y^(6)` + 22680
`x^(9)`
`y^(8)` + 20412
`x^(6)`
`y^(10)` + 10206
`x^(3)`
`y^(12)` + 2187
`y^(14)`

Therefore;

`(2x^(3)+3y^(2)) ^(7)` = 128
`x^(21)` + 1344
`x^(18)`
`y^(2)` + 6048
`x^(15)`
`y^(4)` + 15120
`x^(12)`
`y^(6)` + 22680
`x^(9)`
`y^(8)` + 20412
`x^(6)`
`y^(10)` + 10206
`x^(3)`
`y^(12)` + 2187
`y^(14)`