a Draw a rectangle with the terms of each factor on two sides. Then multiply the terms separately.
B
b Draw a rectangle with the terms of each factor on two sides. Then multiply the terms separately.
C
c Draw a rectangle with the terms of each factor on two sides. Then multiply the terms separately.
D
d Draw a rectangle with the terms of each factor on two sides. Then multiply the terms separately.
A
a 5m^2+9m+2
B
b - x^2+4x+12
C
c 25x^2-10xy+y^2
D
d 6x^2-15xy+12x
Practice makes perfect
a The first part of multiplying using a generic rectangle is to write each term separately. The terms of one factor are placed along one side and the terms of the other factor are placed along the adjacent side.
The product of each term is written inside the rectangle in the square corresponding to the terms. For example, m is multiplied by 5m, and the result, 5m^2, is written as follows.
Let's do this for all corners of the rectangle.
The result of the multiplication is the sum of all terms inside the rectangle.
5m^2+10m-m+2
⇕
5m^2+9m+2
b The rectangle is set up just as the previous exercise, with the terms of one factor along one side and the terms of the other factor along the adjacent side.
By multiplying each pair of terms, we can complete the rectangle.
The product is the sum of all terms inside the rectangle.
- x^2+6x-2x+12
⇕
- x^2+4x+12
c The power (5x-y)^2 can be written as (5x-y)(5x-y), meaning that we can draw the following generic rectangle.
By multiplying each pair of terms, we can complete the rectangle.
The product is the sum of all terms inside the rectangle.
25x^2-5xy-5xy+y^2
⇕
25x^2-10xy+y^2
d Here it's not two binomials that are multiplied, but the procedure is still the same.
The product is the sum of all terms inside the rectangle.
6x^2-15xy+12x
