6: \(-x^2y\left(xy^2-\dfrac{1}{2}xy+\dfrac{3}{4}x^2y^2\right)\)

\(=-x^3y^3+\dfrac{1}{2}x^3y^2-\dfrac{3}{4}x^4y^3\)

7: \(\dfrac{2}{3}x^2y\cdot\left(3xy-x^2+y\right)\)

\(=2x^3y^2-\dfrac{2}{3}x^4y+\dfrac{2}{3}x^2y^2\)

8: \(-\dfrac{1}{2}xy\left(4x^3-5xy+2x\right)\)

\(=-2x^4y+\dfrac{5}{2}x^2y^2-x^2y\)

9: \(2x^2\left(x^2+3x+\dfrac{1}{2}\right)=2x^4+6x^3+x^2\)

10: \(-\dfrac{3}{2}x^4y^2\left(6x^4-\dfrac{10}{9}x^2y^3-y^5\right)\)

\(=-9x^8y^2+\dfrac{5}{3}x^6y^5+\dfrac{3}{2}x^4y^7\)

11: \(\dfrac{2}{3}x^3\left(x+x^2-\dfrac{3}{4}x^5\right)=\dfrac{2}{3}x^3+\dfrac{2}{3}x^5-\dfrac{1}{2}x^8\)

12: \(2xy^2\left(xy+3x^2y-\dfrac{2}{3}xy^3\right)=2x^2y^3+6x^3y^3-\dfrac{4}{3}x^2y^5\)

13: \(3x\left(2x^3-\dfrac{1}{3}x^2-4x\right)=6x^4-x^3-12x^2\)

a) \(3x\left(5x^2-2x-1\right)\)

\(=3x.5x^2-3x.2x+3x.\left(-1\right)\)

\(=15x^3-6x^2-3x\)

b) \(\left(x^3-2xy+3\right)\left(-xy\right)\)

\(=\left(-xy\right).\left(x^2+2xy-3\right)\)

\(=\left(-xy\right).x^2+\left(-xy\right).2xy+\left(-xy\right).\left(-3\right)\)

\(=x^3y-2x^2y^2+3xy\)

mấy câu sau vt lại đè

a: \(\dfrac{\left(x+1\right)}{x^2+2x-3}=\dfrac{\left(x+1\right)}{\left(x+3\right)\cdot\left(x-1\right)}=\dfrac{\left(x+1\right)\left(x+2\right)\left(x+5\right)}{\left(x+3\right)\left(x-1\right)\left(x+2\right)\left(x+5\right)}\)

\(\dfrac{-2x}{x^2+7x+10}=\dfrac{-2x}{\left(x+2\right)\left(x+5\right)}=\dfrac{-2x\left(x+3\right)\left(x-1\right)}{\left(x+2\right)\left(x+5\right)\left(x+3\right)\left(x-1\right)}\)

b: \(\dfrac{x-y}{x^2+xy}=\dfrac{x-y}{x\left(x+y\right)}=\dfrac{y^2\left(x-y\right)}{xy^2\left(x+y\right)}\)

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

c: \(\dfrac{x-2y}{2}=\dfrac{\left(x-2y\right)\left(x-xy\right)}{2\left(x-xy\right)}\)

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

Bài 4

c) x(x - 2) + (x - 2)²

= (x - 2)(x + x - 2)

= (x - 2)(2x - 2)

= 2(x - 2)(x - 1)

d) 2x(x - y)² - 5(y - x)

= 2x(x - y)² + 5(x - y)

= (x - y)(2x + 5)

Bài 5

a) x² - 6x - 2xy + 12y

= (x² - 6x) - (2xy - 12y)

= x(x - 6) - y(x - 6)

= (x - 6)(x - y)

b) 10ax - 5ay - 2x + y

= (10ax - 5ay) - (2x - y)

= 5a(2x - y) - (2x - y)

= (2x - y)(5a - 1)

c) x⁴ + x³y - x - y

= (x⁴ + x³y) - (x + y)

= x³(x + y) - (x + y)

= (x + y)(x³ - 1)

= (x + y)(x - 1)(x² + x + 1)

d) x³ + 2x² - 4x - 8

= (x³ + 2x²) - (4x + 8)

= x²(x + 2) - 4(x + 2)

= (x + 2)(x² - 4)

= (x + 2)(x + 2)(x - 2)

= (x + 2)²(x - 2)

e) xy - 5x - y² + 5y

= (xy - 5x) - (y² - 5y)

= x(y - 5) - y(y - 5)

= (y - 5)(x - y)

f) ax - bx - 2cx - 2a + 2b + 4c

= (ax - bx - 2cx) - (2a - 2b - 4c)

= x(a - b - 2c) - 2(a - b - 2c)

= (a - b - 2c)(x - 2)

g) 5x²y + 5xy² - b²x - b²y

= (5x²y + 5xy²) - (b²x + b²y)

= 5xy(x + y) - b²(x + y)

= (x + y)(5xy - b²)

h) 4x³ - 4x² - 9x + 9

= (4x³ - 4x²) - (9x - 9)

= 4x²(x - 1) - 9(x - 1)

= (x - 1)(4x² - 9)

= (x - 1)(2x - 3)(2x + 3)

Giải cách lớp 7 được không?

được bạn

\(a,=5\left(x-y\right)+a\left(x-y\right)=\left(5+a\right)\left(x-y\right)\\ b,=a\left(x+y\right)+b\left(x+y\right)=\left(a+b\right)\left(x+y\right)\\ c,=x\left(x+1\right)+a\left(x+1\right)=\left(x+a\right)\left(x+1\right)\\ d,Sửa:x^2y+xy^2-3x-3y=xy\left(x+y\right)-3\left(x+y\right)=\left(xy-3\right)\left(x+y\right)\\ e,=xy\left(x+1\right)-\left(x+1\right)=\left(xy-1\right)\left(x+1\right)\\ f,=x^2-4=\left(x-2\right)\left(x+2\right)\\ g,=\left(x+3\right)^2-y^2=\left(x-y+3\right)\left(x+y+3\right)\\ h,=\left(x+5\right)^2-y^2=\left(x-y+5\right)\left(x+y+5\right)\\ i,=\left(x-4\right)^2-24y^2=\left(x-2\sqrt{6}y-4\right)\left(x+2\sqrt{6}y+4\right)\)