Rút gọn các biểu thức sau:
1. (6x+1)2 + (6x-1)2 – 2(1+6x)(6x-1)
2. 3x(x-2) – 5x(1-x) – 5(x2 – 3)
3. (7x-3)(2x+1) – (5x – 2)(x+4) – 9×2 + 17x
4. (6x -5)(x+8) – (3x-1)(2x+3) – 9(4x-3)
Rút gọn các biểu thức sau:
1. (6x+1)2 + (6x-1)2 – 2(1+6x)(6x-1)
2. 3x(x-2) – 5x(1-x) – 5(x2 – 3)
3. (7x-3)(2x+1) – (5x – 2)(x+4) – 9×2 + 17x
4. (6x -5)(x+8) – (3x-1)(2x+3) – 9(4x-3)
Đáp án:
Giải thích các bước giải:
Giải thích các bước giải:
\(\begin{array}{l}
1.\,\,{\left( {6x + 1} \right)^2} + {\left( {6x – 1} \right)^2} – 2\left( {1 + 6x} \right)\left( {6x – 1} \right)\\
= {\left[ {\left( {1 + 6x} \right) – \left( {6x – 1} \right)} \right]^2} = {\left( {1 + 6x – 6x + 1} \right)^2}\\
= 4\\
2.\,\,\,3x\left( {x – 2} \right) – 5x\left( {1 – x} \right) – 5\left( {{x^2} – 3} \right)\\
= 3{x^2} – 6x – 5x + 5{x^2} – 5{x^2} + 15\\
= 3{x^2} – 11x + 15\\
3.\,\,\,\left( {7x – 3} \right)\left( {2x + 1} \right) – \left( {5x – 2} \right)\left( {x + 4} \right) – 9{x^2} + 17x\\
= 14{x^2} – x – 3 – \left( {5{x^2} + 18x – 8} \right) – 9{x^2} + 17x\\
= – 2x + 5\\
4.\,\,\left( {6x – 5} \right)\left( {x + 8} \right) – \left( {3x – 1} \right)\left( {2x + 3} \right) – 9\left( {4x – 3} \right)\\
= 6{x^2} – 43x – 40 – \left( {6{x^2} + 7x – 3} \right) – 36x + 27\\
= – 86x – 10
\end{array}\)