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Practice Finding Squares Using (a + b)²

Worksheet Description

Practice drill on 3-step trick for finding the squares of numbers up to 300 based on the classic algebraic identity (a + b)² = a² + 2ab + b²

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The Worksheet

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Right to left problem flow

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The detailed description of the worksheet

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Introduction

This worksheet helps learners practice a powerful and classic squaring technique based on the algebraic identity (a + b)² = a² + 2ab + b². It is designed to make squaring numbers up to 300 fast, structured, and mentally manageable.

The Algebraic Identity Behind the Trick

The identity (a + b)² = a² + 2ab + b² allows any number to be split into two convenient parts and squared efficiently.

By choosing suitable values for a and b, the squaring process becomes a sequence of three simple calculations instead of a long multiplication.

How the (a + b)² Squaring Method Works

To square a number using this method:

  1. Split the number into two parts: a and b
  2. Calculate
  3. Calculate 2ab
  4. Calculate
  5. Add all three results to get the final square

This structured approach reinforces the connection between algebra and quick mental arithmetic.

Important: Right-to-Left Mental Flow

Unlike many left-to-right quick arithmetic techniques, this squaring method follows a right-to-left mental flow.

You should compute and think in the following order:, then 2ab, and finally .

This order keeps the mental process aligned with how the identity naturally expands and helps reduce calculation errors.

Range of Numbers Covered

The problems in this worksheet cover numbers from 30 to 300.

This range is ideal for practicing squaring beyond basic facts while still keeping calculations mentally accessible.

Using the Show Hint Option

Each problem includes a Show Hint option.

When enabled, the hint reveals the three components of the trick: , 2ab, and , helping learners verify their thinking and build confidence.

Prerequisite Knowledge

A solid understanding of the squares of numbers up to 30 is recommended before attempting this worksheet.

Squares - 1 to 30

12=1
112=121
212=441
22=4
122=144
222=484
32=9
132=169
232=529
42=16
142=196
242=576
52=25
152=225
252=625
62=36
162=256
262=676
72=49
172=289
272=729
82=64
182=324
282=784
92=81
192=361
292=841
102=100
202=400
302=900

Familiarity with these basic squares allows smoother execution and faster mental calculation when applying the identity.

Related Learning Resource

Before starting this worksheet, learners are encouraged to visit the detailed blog post on Finding Squares Using (a + b)², which explains this algebraic trick step by step with clear examples.

Understanding the logic in advance will make practice more effective and enjoyable.

Online, Interactive, and Skill-Focused

This is an online, interactive worksheet where learners enter only the final square into the input box.

Instant feedback allows mistakes to be corrected immediately, supporting rapid improvement. No printing or downloading is required.

Click on the green box in the first problem of the worksheet to get started!!