The solution to the binomial expression by using Pascal's triangle is:
[tex]\mathbf{=177147x^{11}-2598156x^{10}y +17321040x^9y^2-69284160x^8y^3+184757760x^7y^4}[/tex]
[tex]\mathbf{-344881152x^6y^5+459841536x^5y^6-437944320x^4y^7+291962880x^3y^8}[/tex]
[tex]\mathbf{-129761280x2y^9+34603008xy^{10}-4194304y^{11}}[/tex]
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:
[tex]\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}[/tex]
The solution to the expansion of the binomial (3x-4y)^11 can be computed as:
[tex]\mathbf{=177147x^{11}-2598156x^{10}y +17321040x^9y^2-69284160x^8y^3+184757760x^7y^4}[/tex]
[tex]\mathbf{-344881152x^6y^5+459841536x^5y^6-437944320x^4y^7+291962880x^3y^8}[/tex]
[tex]\mathbf{-129761280x2y^9+34603008xy^{10}-4194304y^{11}}[/tex]
Learn more about Pascal's triangle here:
https://brainly.com/question/16978014
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