(2x+3y)⁴
1) let 2x = a and 3y = b
(a+b)⁴ = a⁴ + a³b + a²b² + ab³ + b⁴
Now let's find the coefficient of each factor using Pascal Triangle
0 | 1
1 | 1 1
2 | 1 2 1
3 | 1 3 3 1
4 | 1 4 6 4 1
0,1,2,3,4,.. represent the exponents of binomials
Since our binomial has a 4th exponents, the coefficients are respectively:
(1)a⁴ + (4)a³b + (6)a²b² + (4)ab³ + (1)b⁴
Now replace a and b by their real values in (1):
2⁴x⁴ +(4)8x³(3y) + (6)(2²x²)(3²y²) + (4)(2x)(3³y³) + (1)(3⁴)(y⁴)
16x⁴ + 96x³y + 216x²y² + 216xy³ + 81y⁴
Convert 2 km into cm
1 km = 100,000 cm
2 km = 200,000 cm
therefore 9,000 cm is greater
We know the triangle is an isosceles triangle. So, we use the Pythagorean Theorem.
a^2+b^2=c^2
The c would be 22, because it's the longest edge. Now find a or b. They are the same, that is how you find the two sides of the triangle for part A.
To find the area of the triangle, the forumla is a=hb/2
Plug in the numbers for that formula and the answer would be found for part B.
I hope I helped.
