Đề thi giữa kì 1 Toán 8 Chân trời sáng tạo – Đề 2 (có đáp án)

a) $\left(3xyz-3x^2+5xy-1\right)-\left(5x^2+xyz-5xy+3-y\right)$

$=3xyz-3x^2+5xy-1-5x^2-xyz+5xy-3+y$

$=\left(3xyz-xyz\right)+\left(-3x^2-5x^2\right)+\left(5xy+5xy\right)+y+\left(-1-3\right)$

$=2xyz-8x^2+10xy+y-4$.

b) $\left(3x^3-x^{2}y+2xy+3\right)+\left(x^{2}y-2xy-2\right)$

$=3x^3-x^{2}y+2xy+3+x^{2}y-2xy-2$

$=\left((-x^{2}y)+\left(x^{2}y\right)\right)+(2xy-2xy)+3x^3+(3-2)$

$=3x^3+1$.

c) $(2x{y}^3-4y-8x)\cdot \left(\frac{1}{2}y\right)$

$=2x{y}^3.\left(\frac{1}{2}y\right)+(-4y).\left(\frac{1}{2}y\right)+(-8x).\left(\frac{1}{2}y\right)$

$=x{y}^4-2y^2-4xy$.

d) $\left(x^8{y}^8+2x^5{y}^5+7x^3{y}^3\right):\left(-x^2{y}^2\right)$

$=x^8{y}^8:\left(-x^2{y}^2\right)+2x^5{y}^5:\left(-x^2{y}^2\right)+7x^3{y}^3:\left(-x^2{y}^2\right)$

$=-x^6{y}^6-2x^3{y}^3-7xy$.

a) $2x^3+6x^2-4x=2x\left(x^2+3x-2\right)$

b) ${\left(2x+5\right)}^2-9x^2$

$=\left(2x+5+9x\right)\left(2x+5-9x\right)$

$=\left(11x+5\right)\left(5-7x\right)$

c) $4x^2-9y^2+4x-6y$

$=\left(4x^2-9y^2\right)+\left(4x-6y\right)$

$=\left(2x+3y\right)\left(2x-3y\right)+2\left(2x-3y\right)$

$=\left(2x-3y\right)\left(2x+3y+2\right)$.

a) Điều kiện xác định của biểu thức A là $x\ne 3;x\ne \pm 6$ .

b) Với $x\ne 3;x\ne \pm 6$ , ta có:

$A=\left(\frac{x}{x^2-36}+\frac{6-x}{6x+x^2}\right):\frac{2x-6}{x^2+6x}+\frac{x}{6-x}$

$=\left[\frac{x}{\left(x+6\right)\left(x-6\right)}+\frac{6-x}{x\left(x+6\right)}\right]:\frac{2\left(x-3\right)}{x\left(x+6\right)}+\frac{x}{6-x}$

$=\left[\frac{x^2}{x\left(x+6\right)\left(x-6\right)}-\frac{{\left(x-6\right)}^2}{x\left(x+6\right)\left(x-6\right)}\right]\cdot \frac{x\left(x+6\right)}{2\left(x-3\right)}+\frac{x}{6-x}$

$=\frac{x^2-\left(x^2-12x+36\right)}{x\left(x+6\right)\left(x-6\right)}\cdot \frac{x\left(x+6\right)}{2\left(x-3\right)}+\frac{x}{6-x}$

$=\frac{x^2-x^2+12x-36}{2\left(x-3\right)\left(x-6\right)}+\frac{x}{6-x}$

$=\frac{12x-36}{2\left(x-3\right)\left(x-6\right)}+\frac{x}{6-x}$

$=\frac{12\left(x-3\right)}{2\left(x-3\right)\left(x-6\right)}-\frac{x}{x-6}$

$=\frac{6}{x-6}-\frac{x}{x-6}=\frac{6-x}{x-6}=-1$.