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The Quadratic Identities
The Quadratic Identities
There are 3 identities that you will need to know:
There are 3 identities that you will need to know:
- (a + b)² = a² + 2ab + b²
- (a − b)² = a² − 2ab + b²
- (a − b)(a + b) = a² − b²
The diagrams below show the geometrical proof for the first two.
The diagrams below show the geometrical proof for the first two.
Explore!
Explore!
Move the slide for a visual proof of the algebraic identity for the difference of 2 squares.
Move the slide for a visual proof of the algebraic identity for the difference of 2 squares.
Test Yourself! (Level 1)
Test Yourself! (Level 1)
Use the applet below to generate random practice questions to check your understanding of expanding and factorising quadratic expressions using the algebraic identities.
Use the applet below to generate random practice questions to check your understanding of expanding and factorising quadratic expressions using the algebraic identities.
Use the Purple Slider to toggle difficulty.
Use the Purple Slider to toggle difficulty.
Use the Green Slider to switch the question types from Expansion to Factorisation to Random Mode.
Use the Green Slider to switch the question types from Expansion to Factorisation to Random Mode.
Check the check box to see the hint and answers.
Check the check box to see the hint and answers.
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