Bài tập theo tuần Toán 8 - Tuần 10 (Đề 1)

Đáp án B

Đáp án D

Đáp án B

Đáp án A

1 - b

2 - a

3 - c

4 - d

$\begin{array}{l}{85}^2+{15}^2+85.30\\ ={85}^2+\mathrm{2.85.15}+{15}^2\\ ={\left(85+15\right)}^2={100}^2=10000\end{array}$

$\begin{array}{l}\left(12{\mathrm{x}}^3\mathrm{y}+3\mathrm{xy}-4{\mathrm{x}}^2{\mathrm{y}}^2\right):4\mathrm{xy}\\ =\left(12{\mathrm{x}}^3\mathrm{y}:4\mathrm{xy}\right)+\left(3\mathrm{xy}:4\mathrm{xy}\right)-\left(4{\mathrm{x}}^2{\mathrm{y}}^2:4\mathrm{xy}\right)\\ =3{\mathrm{x}}^2+\frac{3}{4}-\mathrm{xy}\end{array}$

${\mathrm{x}}^2+5\mathrm{x}=\mathrm{x}\left(\mathrm{x}+5\right)$

$\begin{array}{l}-{\mathrm{x}}^2+2\mathrm{x}+2\mathrm{y}+{\mathrm{y}}^2=\left({\mathrm{y}}^2-{\mathrm{x}}^2\right)+\left(2\mathrm{x}+2\mathrm{y}\right)\\ =\left(\mathrm{x}+\mathrm{y}\right)\left(\mathrm{y}-\mathrm{x}\right)+2\left(\mathrm{x}+\mathrm{y}\right)=\left(\mathrm{x}+\mathrm{y}\right)\left(\mathrm{y}-\mathrm{x}+2\right)\end{array}$

$$\begin{gathered} \begin{array}{l}\left(\mathrm{x}-2\right)\left(\mathrm{x}+5\right)-\left(\mathrm{x}-3\right)\left(\mathrm{x}+3\right)=5\\ {\mathrm{x}}^2+3\mathrm{x}-10-{\mathrm{x}}^2+9=5\\ 3\mathrm{x}=6\Rightarrow \mathrm{x}=2\end{array} \\ \mathrm{Vậy}: \mathrm{x}=2 \end{gathered}$$

Sau khi đặt phép chia, ta được thương: ${\mathrm{n}}^2-2\mathrm{n}+1$và dư là 5

Để $\left(3{\mathrm{n}}^3-7{\mathrm{n}}^2+5\mathrm{n}+6\right)⋮\left(3\mathrm{n}-1\right)$ thì $\frac{5}{3\mathrm{n}-1}\in \mathrm{\mathbb{Z}}$

$\Rightarrow \left(3\mathrm{n}-1\right)\in \left(5\right)=\left\{\pm 1;\pm 5\right\}\Rightarrow \mathrm{n}\in \left\{\frac{2}{3};0;2;\frac{4}{3}\right\} \mathrm{mà} \mathrm{n} \mathrm{là} \mathrm{số} \mathrm{nguyên} \mathrm{nên} \mathrm{n}\in \left\{0;2\right\}$