Algebra · Algebraic proof
Chapter 1 · 4
The idea
Proofs with squares
The square-shaped proof toolkit: expanding (an + b)² honestly, reading parity out of 2(…) + 1, difference-of-two-squares shortcuts, and the completed square as an always-positive argument.
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Algebra · Algebraic proof
Proofs with squares
The square-shaped proof toolkit: expanding (an + b)² honestly, reading parity out of 2(…) + 1, difference-of-two-squares shortcuts, and the completed square as an always-positive argument.
Why it works
One expansion carries everything
The grade-8 proof questions look endlessly varied — "prove it's odd", "prove it's a multiple of 20", "prove it's positive for all " — but almost every one crowns the same three square-shaped arguments. And all three live or die on one expansion: — middle term included, every time.Parity: exhibit 2(…) or 2(…) + 1
Even means whole; odd means one more than that. The square of any even number: — even (in fact a multiple of 4). The proof's final move is always rewriting into the parity shape and saying which it is.Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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