Math Problem Statement

Factorize the expression (a + b)(c + d) using the distributive property.

Solution

The image you provided seems to describe a mathematical expression related to the area of a rectangle or rectangular shape, where "长" represents length and "宽" represents width, and the calculation for area involves adding the areas of different faces of a 3D shape.

The formula at the bottom of the image:

(a+b)(c+d)=ac+ad+bc+bd(a + b)(c + d) = ac + ad + bc + bd

is an expansion of a binomial product, showing how to calculate the total area of a rectangular shape by adding up the areas of individual faces.

Would you like to dive deeper into any specific aspect of this formula or have questions on the other sections of the image? Feel free to ask!

Here are some related questions for further exploration:

  1. How do you apply the distributive property in algebra?
  2. Can you calculate the surface area of a rectangular prism using this formula?
  3. What is the significance of breaking down the total area into parts?
  4. How would you expand other binomial expressions like (x+y)(a+b)(x + y)(a + b)?
  5. What is the difference between surface area and volume calculations in geometry?

Tip: To simplify the expansion of binomials, always remember the FOIL method (First, Outside, Inside, Last).

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Math Problem Analysis

Mathematical Concepts

Algebra
Distributive Property
Binomial Expansion

Formulas

(a + b)(c + d) = ac + ad + bc + bd

Theorems

Distributive Property of Multiplication

Suitable Grade Level

Grades 7-9