Respuesta :
Answer:
4C0(m⁴)(3⁰) + 4C1(m³)(3¹) + 4C2(m²)(3²) + 4C3(m¹)(3³) + 4C4(m⁰3⁴)
Step-by-step explanation:
Using Pascal's triangle, going to the 4th line down, the coefficients are 1, 4, 6, 4 and 1. This is the same as 4C0, 4C1, 4C2, 4C3, and 4C4.
In these expansions, the exponent for the first term of the binomial will start at 4 and decrease, while the exponent for the second term of the binomial will start at 0 and increase.
This gives us
4C0(m⁴)(3⁰) + 4C1(m³)(3¹) + 4C2(m²)(3²) + 4C3(m¹)(3³) + 4C4(m⁰3⁴).
The expression which is equivalent to the expression [tex](m+3)^{2}[/tex] is [tex]4C_{0} m^{0} 3^{2} +4C_{1} m^{1} 3^{3} +4C_{2} m^{2} 3^{2} +4C_{4} m^{4} 3^{0}[/tex].
What is Pascal's triangle?
Pascal's triangle is triangular arrangement of numbers that gives the coefficients in the expansion of any binomial expression such as [tex](x+y)^{n}[/tex] in such a way that [tex](x+y)^{n} =nC_{0} x^{0} y^{n-0}+ nC_{1} x^{1} y^{n-1}+..............nC_{n} x^{n} y^{0}[/tex]
In which we have to solve for combinations.
How to find expression?
We have been given expression which is [tex](m+3)^{4}[/tex] and we have to expand it and find the equivavlent expression to this expression.
Expression is combination of numbers, symbols, fraction, coefficients, indeterminants.
Equivalent expression refers to that expression which gives same value as the expression whose equivalent expression we found gives.
[tex](m+3)^{4}[/tex]=[tex]4C_{0} m^{0} 3^{4-0} +4C_{1} m^{1} 3^{4-1} +4C_{2} m^{2} 3^{4-2} +4C_{4} m^{4} 3^{0}[/tex]
=[tex]4C_{0} m^{0} 3^{4} +4C_{1} m^{1} 3^{3} +4C_{2} m^{2} 3^{2} +4C_{4} m^{4} 3^{0}[/tex]
Hence the equivalent expression to [tex](m+3)^{4}[/tex] is [tex]4C_{0} m^{0} 3^{4} +4C_{1} m^{1} 3^{3} +4C_{2} m^{2} 3^{2} +4C_{4} m^{4} 3^{0}[/tex].
Learn more about Pascal's triangle at https://brainly.com/question/16978014
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