Question

Use the Binomial Theorem and Pascal’s Triangle to write each binomial expansion.

Answer 1

Answer:

x² + 8x + 16

Step-by-step explanation:

You can draft the Pascal's Triangle as below;

                                             Exponent

                  1-----------------------0

               1     1  -------------------1

             1   2    1 ------------------2

            1  3   3   1 -----------------3

According to the question, we use values for exponent 2 because (a+b)²

Given  (x+4)²...................................expand

x² × 4⁰ + x¹ × 4¹+ x⁰ × 4²

x² × 1 + x × 4 + 1 × 16

x² + 4x + 16---------------------------------introduce values in exponential 2 of the table which are 1  2  1

x² × 1 + 2 × 4x + 16 × 1

⇒ x² + 8x + 16