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Two sets of quadratic expressions are shown below in various forms: Line 1: x2 + 3x + 2 (x + 1)(x + 2) (x + 1.5)2 − 0.25 Line 2: x2 + 5x + 6 (x + 2)(x + 3) (x + 2.5)2 + 6.25 Which line contains three equivalent expressions? Line 1 only Line 2 only Both Line 1 and Line 2 Neither Line 1 nor Line 2
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expand or factorise the second and third of each line to see whether they are equal to the first. Let me do the first line: (x+1)(x+2)=x^2 + 2x + x + 2 = x^2+3x+2 (x+1.5)^2 - 0.25= (x+1.5+0.5)(x+1.5-0.5)=(x+2)(x+1) So the first line is correct. For the third term I factorise instead of expanding.
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