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Sublime Maths Worksheets

Finding squares using the identity (a + b)²

This mathematics trick helps you calculate the squares of the numbers in your mind using just digits and carries — no calculator needed! Once it is learnt, you can easily write down the squares of the numbers up to 300.

What you need to know before you start...

You need to master Multiplication Tables (1 to 20) and Squares (1 to 30). Memorizing these essential concepts is crucial for any mathematics student. Our specially crafted worksheets on Multiplication and Squares will help you solidify this knowledge. Not only will it benefit this blog post, but it will also prove invaluable for numerous other topics covered on our blog.
Use the Times Tables Reference to learn and memorize.

The Trick

This 3-step technique is based on the classic algebraic identity:

(a + b)2 = a2 + 2ab + b2

But instead of calculating the whole expression at once, we split the number into digits and apply three steps.

Choose a number

The 3 steps are...

Finding 642Break the given number 64 into 2 parts a and b: First part (up to tens place): 6 = aSecond part (units place): 4 = b

  1. Step 1: b2
    Square the second part b(4)
    42 = 16, write 6 here and carry 1 to next step
    Partial answer is ???6
  2. Step 2: 2ab
    Multiply the two parts by 2 and add carry from previous step2 ✕ 6 ✕ 4 = 48
    48 + 1 = 49, write 9 here and carry 4 to next step
    Partial answer is ??96
  3. Step 3: a2
    Square the first part a(6) and add carry from previous step
    62 + 4 = 36 + 4 = 40, write 40 here
    Final answer is 4096
642 = 4096

Solution for all the given numbers

StepFinding 282Carry OverAnswer
182 = 646??4
2(2 ✕ 2 ✕ 8) + 6 = 383?84
322 + 3 = 7 784
StepFinding 392Carry OverAnswer
192 = 818???1
2(2 ✕ 3 ✕ 9) + 8 = 626??21
332 + 6 = 15 1521
StepFinding 472Carry OverAnswer
172 = 494???9
2(2 ✕ 4 ✕ 7) + 4 = 606??09
342 + 6 = 22 2209
StepFinding 552Carry OverAnswer
152 = 252???5
2(2 ✕ 5 ✕ 5) + 2 = 525??25
352 + 5 = 30 3025
StepFinding 642Carry OverAnswer
142 = 161???6
2(2 ✕ 6 ✕ 4) + 1 = 494??96
362 + 4 = 40 4096
StepFinding 712Carry OverAnswer
112 = 10???1
2(2 ✕ 7 ✕ 1) + 0 = 141??41
372 + 1 = 50 5041
StepFinding 832Carry OverAnswer
132 = 90???9
2(2 ✕ 8 ✕ 3) + 0 = 484??89
382 + 4 = 68 6889
StepFinding 922Carry OverAnswer
122 = 40???4
2(2 ✕ 9 ✕ 2) + 0 = 363??64
392 + 3 = 84 8464
StepFinding 1082Carry OverAnswer
182 = 646????4
2(2 ✕ 10 ✕ 8) + 6 = 16616???64
3102 + 16 = 116 11664
StepFinding 1122Carry OverAnswer
122 = 40????4
2(2 ✕ 11 ✕ 2) + 0 = 444???44
3112 + 4 = 125 12544
StepFinding 1362Carry OverAnswer
162 = 363????6
2(2 ✕ 13 ✕ 6) + 3 = 15915???96
3132 + 15 = 184 18496
StepFinding 1482Carry OverAnswer
182 = 646????4
2(2 ✕ 14 ✕ 8) + 6 = 23023???04
3142 + 23 = 219 21904
StepFinding 1522Carry OverAnswer
122 = 40????4
2(2 ✕ 15 ✕ 2) + 0 = 606???04
3152 + 6 = 231 23104
StepFinding 1632Carry OverAnswer
132 = 90????9
2(2 ✕ 16 ✕ 3) + 0 = 969???69
3162 + 9 = 265 26569
StepFinding 1752Carry OverAnswer
152 = 252????5
2(2 ✕ 17 ✕ 5) + 2 = 17217???25
3172 + 17 = 306 30625
StepFinding 2242Carry OverAnswer
142 = 161????6
2(2 ✕ 22 ✕ 4) + 1 = 17717???76
3222 + 17 = 501 50176
StepFinding 2582Carry OverAnswer
182 = 646????4
2(2 ✕ 25 ✕ 8) + 6 = 40640???64
3252 + 40 = 665 66564