Question

[Hàn Vũ]

1. Viết các biểu thức sau dưới dạng tổng:

a: (a - b²) × (a + b²)

b: (a² + 2a + 3) × (a² + 2a - 3)

c: (a² + 2a +3) × (a² - 2a - 3)

d: (a² - 2a + 3) × (a² + 2a -3)

e: (-a² - 2a + 3) × (-a² - 2a +3)

g: (a² + 2a +3) × (a² - 2a +3)

f: (a² + 2a) × (2a - a²)

2. Viết các biểu thức sau dưới dạng tổng:

a: (x + 1) × (x² - x +1)

b: (x + y + z)²

c: (x - y + z)²

d: (x - 2y) × (x² + 2xy + 4y²)

e: (x - y - z)²

Answer 1

[Nguyễn Thị Diễm Quỳnh]

Bài 1:

a) \(\left(a-b^2\right)\left(a+b^2\right)=a^2-b^4\)

b) \(\left(a^2+2a-3\right)\left(a^2+2a+3\right)=\left(a^2+2a\right)^2-9\)

c) \(\left(a^2+2a+3\right)\left(a^2-2a-3\right)=a^2-\left(2a+3\right)^2\)

d) \(\left(a^2-2a+3\right)\left(a^2+2a+3\right)=9-\left(a^2-2a\right)^2\)

e) \(\left(-a^2-2a+3\right)\left(-a^2-2a+3\right)=\left(-a^2-2a+3\right)^2\)

g) \(\left(a^2+2a+3\right)\left(a^2-2a+3\right)=\left(a^2+3\right)^2-4a^2\)

f) \(\left(a^2+2a\right)\left(2a-a^2\right)=4a^2-a^4\)

Answer 2

[Nguyễn Thị Diễm Quỳnh]

Bài 2 :

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

b) \(\left(x+y+z\right)^2=\left(x+y+z\right)\left(x+y+z\right)=x^2+xy+xz+yx+y^2+yz+zx+zy+z^2=x^2+2xy+2yz+2xz+y^2+z^2\)

c) \(\left(x-y+z\right)^2=\left(x-y+z\right)\left(x-y+z\right)=x^2-xy+xz-xy+y^2-yz+xz-yz+z^2=x^2+y^2+z^2-2xy+2xz-2yz\)d) \(\left(x-2y\right)\left(x^2+2xy+4y^2\right)=\left(x-2y\right)^3\)

e) \(\left(x-y-z\right)^2=\left(x-y-z\right)\left(x-y-z\right)=x^2-xy-xz-xy+y^2+yz-xz+yz+z^2=x^2-2xy-2xz+2yz+y^2+z^2\)