Question

Use Pascal’s Triangle to expand the binomial.

(8v + s)5

Answer 1

1 5 10 10 5 1

Answer 2

1(8v)^5(s)^0 + 5(8v)^4(s)^1 + 10(8v)^3(s)^2 + 10(8v)^2(s)^3 + 5(8v)^1(s)^4 + 1(8v)^0(s)^5

Answer 3

I'm sorry for this long-winded response. If you already have a good understanding of Pascal's Triangle then you can ignore this message.

Pascal's triangle gives us a few things.
It gives us the coefficients on each term,
and it gives us the degree of each term.

Here's a quick example,\[\large (x+y)^2\]The third row of Pascal's triangle corresponds to a binomial of degree 2.
1
1 1
1 2 1 <- The numbers represent the coefficient on each term.

See how we have 3 coefficients? There will be 3 terms.
This is ALWAYS the case with binomials. Whatever the degree of your binomial is, you will have ONE MORE term than that number.

We also get the degree of each term. Let me show you with this example real quick,\[\large (x+y)^2 \quad = \quad 1\cdot x^2y^0+2\cdot x^1y^1+1\cdot x^0y^2\]\[\large \qquad \quad \qquad \;\;= \quad x^2+2xy+y^2\]
See how the degree of the X's count DOWN? And the degree of the Y's count UP? That pattern holds true for all binomials. For a 5th degree binomial, The first term will count DOWN from 5, and the second term will count UP toward five.

Answer 4

@jennychan12 my answer choices are
s5 + 320s4v + 5,120s3v2 + 40,960s2v3 + 16,380sv4 + 26,2144v5
s5 – 5s4v + 10s3v2 – 10s2v3 + 5sv4 – v5
s5 + 40s4 + 640s3 +5,120s2 + 20,480s +32,768
s5 + 40s4v + 640s3v2 + 5,120s2v3 + 20,480sv4 + 32,768v5

Answer 5

and wow, thank you for that explanation zepdrix

Answer 6

uhh, you can multiply it out?
and the answer is one of those answer choices....