The solution to the binomial expression by using Pascal's triangle is:
![\mathbf{=177147x^{11}-2598156x^{10}y +17321040x^9y^2-69284160x^8y^3+184757760x^7y^4}](https://tex.z-dn.net/?f=%5Cmathbf%7B%3D177147x%5E%7B11%7D-2598156x%5E%7B10%7Dy%20%2B17321040x%5E9y%5E2-69284160x%5E8y%5E3%2B184757760x%5E7y%5E4%7D)
![\mathbf{-344881152x^6y^5+459841536x^5y^6-437944320x^4y^7+291962880x^3y^8}](https://tex.z-dn.net/?f=%5Cmathbf%7B-344881152x%5E6y%5E5%2B459841536x%5E5y%5E6-437944320x%5E4y%5E7%2B291962880x%5E3y%5E8%7D)
![\mathbf{-129761280x2y^9+34603008xy^{10}-4194304y^{11}}](https://tex.z-dn.net/?f=%5Cmathbf%7B-129761280x2y%5E9%2B34603008xy%5E%7B10%7D-4194304y%5E%7B11%7D%7D)
<h3>How can we use Pascal's triangle to expand a binomial expression?</h3>
Pascal's triangle can be used to calculate the coefficients of the expansion of (a+b)ⁿ by taking the exponent (n) and adding the value of 1 to it. The coefficients will correspond with the line (n+1) of the triangle.
We can have the Pascal tree triangle expressed as follows:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
--- --- --- --- --- --- --- --- --- --- --- --- --- --- ---
From the given information:
The expansion of (3x-4y)^11 will correspond to line 11.
Using the general formula for the Pascal triangle:
![\mathbf{(a+b)^n = c_oa^nb^0 + c_1 a^{n-1}b^1+c_{n-1}a^1b^{n-1}+c_na^0b^n}](https://tex.z-dn.net/?f=%5Cmathbf%7B%28a%2Bb%29%5En%20%3D%20c_oa%5Enb%5E0%20%2B%20c_1%20a%5E%7Bn-1%7Db%5E1%2Bc_%7Bn-1%7Da%5E1b%5E%7Bn-1%7D%2Bc_na%5E0b%5En%7D)
The solution to the expansion of the binomial (3x-4y)^11 can be computed as:
![\mathbf{=177147x^{11}-2598156x^{10}y +17321040x^9y^2-69284160x^8y^3+184757760x^7y^4}](https://tex.z-dn.net/?f=%5Cmathbf%7B%3D177147x%5E%7B11%7D-2598156x%5E%7B10%7Dy%20%2B17321040x%5E9y%5E2-69284160x%5E8y%5E3%2B184757760x%5E7y%5E4%7D)
![\mathbf{-344881152x^6y^5+459841536x^5y^6-437944320x^4y^7+291962880x^3y^8}](https://tex.z-dn.net/?f=%5Cmathbf%7B-344881152x%5E6y%5E5%2B459841536x%5E5y%5E6-437944320x%5E4y%5E7%2B291962880x%5E3y%5E8%7D)
![\mathbf{-129761280x2y^9+34603008xy^{10}-4194304y^{11}}](https://tex.z-dn.net/?f=%5Cmathbf%7B-129761280x2y%5E9%2B34603008xy%5E%7B10%7D-4194304y%5E%7B11%7D%7D)
Learn more about Pascal's triangle here:
brainly.com/question/16978014
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The answer is B 4 hot dogs = $20 and two hamburgers = $12 so 20 plus 12 equals 32 so the answer is B
You would have more than $102.
Earning 2% a year in interest would get you $2 in interest the very first year:
100(0.02) = 2
Adding this to the amount in the account, you would have 100+2 = 102 after the first year.
0.43 =
3/100 = 0.03
+
4/10 = 0.4
0.03 + 0.4 = 0.43.
Hope this helped☺☺
The greatest common factor of 32 and 52 is: 4
Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 52: 1, 2, 4, 13, 26
The common factors between them are 1, 2, 4, but the greatest common factor between them is 4.