Toán Lớp 8: 25(x-3)^2-(2x-7)^2 81(x+7)^2-(3x+8)^2 49(x-5)^2-(x+4)^2 36(x-y)^2-25(2x-1)^2 (a-5b)^2-16b^2 biến đổi về dạng tích

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1. Giải đáp:

   $\begin{array}{l}
   a)\\
   25{\left( {x – 3} \right)^2} – {\left( {2x – 7} \right)^2}\\
    = {\left( {5x – 15} \right)^2} – {\left( {2x – 7} \right)^2}\\
    = \left( {5x – 15 – 2x + 7} \right)\left( {5x – 15 + 2x – 7} \right)\\
    = \left( {3x – 8} \right)\left( {7x – 22} \right)\\
   b)\\
   81{\left( {x + 7} \right)^2} – {\left( {3x + 8} \right)^2}\\
    = {\left( {9x + 63} \right)^2} – {\left( {3x + 8} \right)^2}\\
    = \left( {9x + 63 + 3x + 8} \right)\left( {9x + 63 – 3x – 8} \right)\\
    = \left( {12x + 72} \right)\left( {6x + 55} \right)\\
   c)\\
   49{\left( {x – 5} \right)^2} – {\left( {x + 4} \right)^2}\\
    = {\left( {7x – 35} \right)^2} – {\left( {x + 4} \right)^2}\\
    = \left( {7x – 35 – x – 4} \right)\left( {7x – 35 + x + 4} \right)\\
    = \left( {6x – 41} \right)\left( {8x – 31} \right)\\
   d)\\
   36{\left( {x – y} \right)^2} – 25{\left( {2x – 1} \right)^2}\\
    = {\left( {6x – 6y} \right)^2} – {\left( {10x – 5} \right)^2}\\
    = \left( {6x – 6y – 10x + 5} \right)\left( {6x – 6y + 10x – 5} \right)\\
    = \left( {5 – 4x – 6y} \right)\left( {16x – 6y – 5} \right)\\
   e){\left( {a – 5b} \right)^2} – 16{b^2}\\
    = {\left( {a – 5b} \right)^2} – {\left( {4b} \right)^2}\\
    = \left( {a – 5b – 4b} \right)\left( {a – 5b + 4b} \right)\\
    = \left( {a – 9b} \right)\left( {a – b} \right)
   \end{array}$

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