Special Products And Factorization — Flashcards

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Use the square of sum formula: (a + b)^2 = a^2 + 2ab + b^2 Step 1: Take a = 2a and b = 3b Step 2: Square the first term: (2a)^2 = 4a^2 Step 3: Middle term: 2(2a)(3b) = 12ab Step 4: Square the second …

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Use the general product pattern or direct multiplication. Step 1: Square the first term: (5x)(5x) = 25x^2 Step 2: Middle terms: (5x)(-6) + (-8)(5x) = -30x - 40x = -70x Step 3: Last terms: (-8)(-6) = …

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Use the product with common term formula: (x + a)(x + b) = x^2 + (a + b)x + ab Step 1: Here a = 9 and b = 3 Step 2: x^2 term stays x^2 Step 3: Middle term = (9 + 3)x = 12x Step 4: Constant term = 9 ×…

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Use the pattern from the product with common term: (x - a)(x - b) = x^2 - (a + b)x + ab Why the middle term is negative: The two negative signs create a negative sum in the middle term, but the cons…

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Use difference of squares. Step 1: Write the numbers around 60 64 × 56 = (60 + 4)(60 - 4) Step 2: Apply (a + b)(a - b) = a^2 - b^2 = 60^2 - 4^2 Step 3: Calculate = 3600 - 16 = 3584 Answer: 3584…

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Expand both squares: (a + b)^2 = a^2 + 2ab + b^2 (a - b)^2 = a^2 - 2ab + b^2 Add them: (a + b)^2 + (a - b)^2 = 2a^2 + 2b^2 = 2(a^2 + b^2) The middle terms cancel because one is +2ab and the other is…

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Expand both squares first: (a + b)^2 = a^2 + 2ab + b^2 (a - b)^2 = a^2 - 2ab + b^2 Subtract: (a + b)^2 - (a - b)^2 = 4ab Answer: 4ab…

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Use the cube of sum formula: (a + b)^3 = a^3 + 3ab(a + b) + b^3 Example: (2x + 3y)^3 Step 1: a = 2x, b = 3y Step 2: a^3 = 8x^3 Step 3: 3ab(a + b) = 3(2x)(3y)(2x + 3y) Step 4: Expanding gives 36x^2y +…