In math, the product is the result you get when you multiply numbers (or algebraic expressions) together, and the numbers you multiply are called factors.

Quick Scoop: Core Idea

  • “Product” goes with multiplication, not addition, subtraction, or division.
  • Example: 3×4=123\times 4=123×4=12. Here, 3 and 4 are factors, and 12 is the product.
  • In algebra, something like x(2+x)x(2+x)x(2+x) is also called a product, because it tells you xxx and (2+x)(2+x)(2+x) are to be multiplied.

Simple Examples

  • 5×5=255\times 5=255×5=25 → product is 25.
  • 2×3×4=242\times 3\times 4=242×3×4=24 → product is 24; 2, 3, and 4 are factors.
  • 6×0=06\times 0=06×0=0 → any number times 0 has product 0.
  • 7×1=77\times 1=77×1=7 → any number times 1 has product equal to the original number.

You can also think of the product as repeated addition:

  • 4×54\times 54×5 is the same as 5+5+5+5=205+5+5+5=205+5+5+5=20, so the product is 20.

Beyond Numbers: Other “Products”

  • In algebra, a “product” can mean the whole multiplication expression, like 3x3x3x or x(2+x)x(2+x)x(2+x), not just the final number.
  • In set theory, a Cartesian product of sets AAA and BBB, written A×BA\times BA×B, is the set of all ordered pairs (a,b)(a,b)(a,b) with a∈Aa\in Aa∈A and b∈Bb\in Bb∈B; this is another use of the word “product” in math.

Tiny Story to Remember It

Imagine you have 3 bags, and each bag has 4 marbles.
You could count: 4 + 4 + 4 = 12.
Or you multiply: 3×4=123\times 4=123×4=12.
That 12 is the product of 3 and 4—your total marbles in all the bags.

TL;DR: In math, “product” means the result of multiplying factors together (like 3 × 4 = 12), and in more advanced contexts it also names certain multiplication-like constructions, such as Cartesian products of sets.

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