Nichols Martin
05/01/2024 · Primary School
14 (a) When \( a=1, b=\frac{1}{3} \) and \( a=\frac{3}{4}, b=\frac{1}{2} \), calculate the values of \( a^{2}-2 a b+b^{2} \) and \( (a-b)^{2} \) respectively. Observe the values of the algebraic expressions. What do you find? What pattern can you guess? (b) Using the pattern you identified, calculate: \( 101.23^{2}-2 \times 101.23 \times 1.23+1.23^{2} \)
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The pattern shows \( a^2 - 2ab + b^2 = (a-b)^2 \). Using this, \( 101.23^2 - 2 \times 101.23 \times 1.23 + 1.23^2 = 10000 \).
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