Question

Use Pascal’s Triangle to determine the third term of the expansion of (x + 3)4.

Answer 1

Answer:

In the Pascal Expansion of $(x+3)^4$ the third term is $54x^2$.

Step-by-step explanation:

Here, the given expression is given as $(x+3)^4$

Now, by the PASCAL'S TRIANGLE EXPANSION:

$(a + b)^4 = 1(a)^4 + 4(a)^3b + 6(a)^2b^2 + 4(a)b^3 + 1b^4\\= 1 + 4b + 6a^2 + 4b^3 + b^4.$

Substituting a  = x and b = 3, we get:

$(x + 3)^4 = 1(x)^4 + 4(x)^3(3) + 6(x)^2(3)^2 + 4(x)(3)^3 + 1(3)^4\\= x^4 + 12x^3 + 54x^2  + 108x+ 81$

In the given expansion, the third term is $54x^2$.

Hence, in the Pascal Expansion of $(x+3)^4$ the third term is $54x^2$.