Introduction to Multiplying Binomials using Partial Products

Have you ever done this:
3 x 48 = 3(40) + 3(8)
= 120 + 24
= 144

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Partial Products: taught in 4th grade

I can split up the number sentence for 2 Digit x 1 Digit Multiplication and complete in PARTS to get the final PRODUCT.

• Make a rectangle. Break up the 2 digit number into tens and ones.

• Put the one digit number on the left side.

Step 1: Break up the 2 digit number into tens and ones.

Step 2: Multiply the one digit number by each part of the 2 digit number.

Step 3: Add the products.

Created by HISD Curriculum using Google Slides

Let’s use base ten blocks to represent 21 x 34.

Step 2:
Multiply:
10 x 10 = 100
10 x 1 = 10
1 x 1 = 1

10

10

1

10

10

10

11 1 1

Base-Ten Blocks by HISD Curriculum using 1,2,3 Math Fonts

Created by HISD Curriculum using Google Slides

Now, let’s use partial product strategy to solve 21 x 34.

Jacob unpacked 21 boxes of baseball cards to display in a sports
store. Each box had 34 cards. How many cards did Jacob unpack?

When we use partial products, we can multiply 21 x 34 by
decomposing each number. Then, add the numbers to find
the product.

Image created by HISD Curriculum using Microsoft Word

Now the same thing, but there will be variables.

Multiply (a - b)(a - b)

that's (a-b) times itself! So...
(a-b)²

(a-b)(a-b)=

a*a -a*b -b*a + -b*-b

a² -2ab + b²

(a-b)(a-b)=