Expand (5 + z)4
choices are:

625 + 500z + 150z2 + 20z3 + z4

625 + 375z + 150z2 + 15z3 + z4

625 + 250z + 100z2 + 10z3 + z4

625 + 125z + 25z2 + 5z3 + z4

A

Step-by-step explanation:

We want to expand: . We need to use the Binomial Theorem for this, which states that for a monic expression like x + k (where k is a constant) to the nth power, the coefficients of the terms will follow the terms in the nth row of the Pascal Triangle. These terms in the Pascal Triangle are of the form:

nC0 , nC1 , nC2 , .... , nC(n - 1) , nCn    ----  here, nCk is combinations: , where ! denotes factorial

So, since the power here is 4, we will be using: 4C0, 4C1, 4C2, 4C3, and 4C4 as our coefficients of the terms.

Let's make 5 + z into z + 5. Now, we expand:

4C0 = 1 , 4C1 = 4 , 4C2 = 6 , 4C3 = 4 , and 4C4 = 1:

Thus, the answer is A.

Hope this helps!

Option 1

625 + 500z + 150z² + 20z³ + z⁴

Step-by-step explanation:

(5 + z)⁴

4C0×5⁰×z⁴ + 4C1×5¹×z³ + 4C2×5²×z² + 4C3×5³×z¹ + 4C4×5⁴×z⁰

z⁴ + 20z³ + 150z² + 500z + 625

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1