làm mấy câu cũng được, làm hết càng tốt
1. 1.3(x+1)^2-(x-1)^2
2. x^2- 2x- 4y^2-4y
3. x^2+ 7x-8
4. x^3-2x^2+x-xy^2
5. (x+4)^2+ (3-x).(3+x)=7
6. Rút gọn phân thức này
2ax^2-4ax+2a
——————–
5b-5bx^2
làm mấy câu cũng được, làm hết càng tốt
1. 1.3(x+1)^2-(x-1)^2
2. x^2- 2x- 4y^2-4y
3. x^2+ 7x-8
4. x^3-2x^2+x-xy^2
5. (x+4)^2+ (3-x).(3+x)=7
6. Rút gọn phân thức này
2ax^2-4ax+2a
——————–
5b-5bx^2
Đáp án:
$\begin{array}{l}
1)3.{\left( {x + 1} \right)^2} – {\left( {x – 1} \right)^2}\\
= {\left( {\sqrt 3 x + \sqrt 3 } \right)^2} – {\left( {x – 1} \right)^2}\\
= \left( {\sqrt 3 x + \sqrt 3 – x + 1} \right)\left( {\sqrt 3 x + \sqrt 3 + x – 1} \right)\\
= \left[ {\left( {\sqrt 3 – 1} \right).x + \left( {\sqrt 3 + 1} \right)} \right].\left[ {\left( {\sqrt 3 + 1} \right).x + \left( {\sqrt 3 – 1} \right)} \right]\\
2){x^2} – 2x – 4{y^2} – 4y\\
= {x^2} – 4{y^2} – 2x – 4y\\
= \left( {x – 2y} \right)\left( {x + 2y} \right) – 2\left( {x + 2y} \right)\\
= \left( {x + 2y} \right)\left( {x – 2y – 2} \right)\\
3){x^2} + 7x – 8\\
= {x^2} + 8x – x – 8\\
= \left( {x + 8} \right)\left( {x – 1} \right)\\
4){x^3} – 2{x^2} + x – x{y^2}\\
= x\left( {{x^2} – 2x + 1 – {y^2}} \right)\\
= x.\left( {x – 1 – y} \right)\left( {x – 1 + y} \right)\\
5){\left( {x + 4} \right)^2} + \left( {3 – x} \right)\left( {3 + x} \right) = 7\\
\Rightarrow {x^2} + 8x + 16 + 9 – {x^2} = 7\\
\Rightarrow 8x = – 18\\
\Rightarrow x = \dfrac{{ – 9}}{4}\\
Vay\,x = \dfrac{{ – 9}}{4}\\
6)\dfrac{{2a{x^2} – 4ax + 2a}}{{5b – 5b{x^2}}}\\
= \dfrac{{2a\left( {{x^2} – 2x + 1} \right)}}{{ – 5b\left( {{x^2} – 1} \right)}}\\
= \dfrac{{2a{{\left( {x – 1} \right)}^2}}}{{ – 5b\left( {x – 1} \right)\left( {x + 1} \right)}}\\
= \dfrac{{2a\left( {x – 1} \right)}}{{ – 5b\left( {x + 1} \right)}}\\
= \dfrac{{ – 2ax – 2a}}{{ – 5bx – 5b}}
\end{array}$