Expansion Intuition Math Example 1

Follow the full solution, then compare it with the other examples linked below.

easy

Expand

(x + 3)(x + 5)

1
Use FOIL: First: $x \cdot x = x^2$ . Outer: $x \cdot 5 = 5x$ . Inner: $3 \cdot x = 3x$ . Last: $3 \cdot 5 = 15$ .
2
Combine: $x^2 + 5x + 3x + 15 = x^2 + 8x + 15$ .
3
Notice: $3 + 5 = 8$ (middle coefficient) and $3 \times 5 = 15$ (constant).

Answer

x^2 + 8x + 15

Expansion distributes each term in one factor to every term in the other. FOIL is a mnemonic for the four products when multiplying two binomials.

About Expansion Intuition

Understanding algebraic expansion as the process of applying the distributive property to multiply out factors and remove parentheses.

Expand [formula].

Expand [formula].

Expand [formula].