Multiplication Table Pattern Quiz

Exponents and Multiplication

• When two exponential forms with the same base are multiplied, the product is an exponential form with the same base.
• The exponent of the new exponential form is the sum of the exponents of the multiple and multiplier.

Table 2.3: Multiplication Table

• The table shows the multiplication of exponential forms with base 10.
• Each row represents a multiplication problem, with the base number, multiplication, 1st term of multiplication, multiplication form of 1st term, 2nd term of multiplication, multiplication form of 2nd term, product, and exponential form of product.

Table 2.4: Fill-in-the-Blank Table

• This table is similar to Table 2.3, but with a different base (represented by ϯ).
• Students are asked to fill in the table using the same format as Table 2.3.

Product of Exponential Expressions

• The product of two or more exponential expressions with the same base can be expressed as another exponential form of that base.
• The exponent of the product is the sum of all exponents of all expressions in that multiplication form.

Multiplication Rule of Exponents

• The rule of multiplication of exponents states that a^m * a^n = a^(m+n).

Verification of Formula (a+b)^2 = a^2 + 2ab + b^2

• The formula can be verified using a geometric method, such as drawing a square with side length (a+b) and calculating its area.
• The area of the square can be broken down into four parts: the area of a square with side length a, the area of a square with side length b, and the areas of two rectangles with sides a and b.
• The total area of the square is equal to (a+b)^2, which is equal to a^2 + 2ab + b^2.

Individual Tasks

• Construct squares to verify the formula (a+b)^2 = a^2 + 2ab + b^2 using pictures or paper cutting.
• Prove the formula for specific values of a and b, such as m+n, 4x+3, 3x+4y, etc.
• Calculate the squares of various numbers, such as 52, 71, 21, 26, 103, using the formula (a+b)^2 = a^2 + 2ab + b^2.

This quiz challenges you to identify the pattern in a multiplication table and apply it to fill in missing values in a new table. Based on the provided example of using 10 as the base number, you will need to determine the multiplication form of each term and fill in the subsequent table accordingly.