Question

Expanding the expression (21 x 12) by replacing the tens with x's and using FOIL, which result matches the normal integer multiplication method?

a) (2x + 1)(1x + 2)
b) (2x + 1)(2x + 1)
c) (2x + 10)(1x + 10)
d) (2x + 10)(10x + 1)

Answer 1

The correct way to expand the expression (21 x 12) using FOIL that matches normal integer multiplication is (2x + 1)(1x + 2), resulting in the polynomial 2x^2 + 5x + 2, which represents 252 when x is 10.

Step-by-step explanation:

When expanding the expression (21 x 12) by replacing the tens with 'x's and using the FOIL method, the correct option that matches the normal integer multiplication method is (2x + 1)(1x + 2). Below is the FOIL method breakdown for this expression:

• First, multiply the first terms: 2x * 1x = 2x^2.
• Outer, multiply the outer terms: 2x * 2 = 4x.
• Inner, multiply the inner terms: 1 * 1x = 1x.
• Last, multiply the last terms: 1 * 2 = 2.

When you combine these terms, you get: 2x^2 + 4x + 1x + 2, which simplifies to 2x^2 + 5x + 2. This is equivalent to 21 x 12 = 252 when x is replaced with 10.