Question

Expand the binomial middle" class="latex-formula"> using Pascal's Triangle. Show all workings necessary and include how to construct Pascal's Triangle.

Answer 1

Answer:

Solution: x³ + 3x² + 3x + 1

Step-by-step explanation:

Take a look at the following Pascal's Triangle:

(x + y)⁰ =                                1

(x + y)¹ =                             1x + 1y

(x + y)² =                       1x² + 2xy + 1y²

(x + y)³ =                  1x³ + 3x²y + 3xy² + 1y³

(x + y)⁴ =             1x⁴ + 4x³ + 6x²y² + 4xy³ + 1y⁴

As you can see our binomial is '(x + 1)³.' Therefore we expand the expression with respect to the third row in the Pascal's Triangle, (x + y)³ = 1x³ + 3x²y + 3xy² + 1y³. The procedure would be as follows:

(x + 1)³ = 1x³ + 3(x)²1 + 3x(1)² + 1(1)³ = x³ + 3x² + 3x + 1

Answer 2

Pascal's triangle will be shown in the image below. Since we have the binomial (x + 1)^3 (3 mean third row) take the third row and simplify.

1x^3 + 3x^2y + 3xy^2 + 1y^3

~Substitute 1 for y

x^3 + 3x^2 + 3x + 1

Best of Luck!