Question

1) Khai triển các hằng đẳng thức:

a) (3x+4y)²           ;          b) (x² + 1)²           ;          c) (3 - 2y)²          ;          d) (xy²-2)²

2) Viết các đa thức ssau về dạng tích của 2 đa thức:

a) x² - 9          ;          b) 25 - 4y²          ;          c) 9x⁴ - 4y²          ;          d) (x + 1)² - y²

 

Answer 1

Bài 1.

a) ( 3x + 4y )² = ( 3x )² + 2.3x.4y + ( 4y )² = 9x² + 24xy + 16y²

b) ( x² + 1 )² = ( x² )² + 2.x².1 + 1² = x⁴ + 2x² + 1

c) ( 3 - 2y )² = 3² - 2.3.2y + ( 2y )² = 9 - 12y + 4y²

d) ( xy² - 2 )² = ( xy² )² - 2.xy².2 + 2² = x²y⁴ - 4xy² + 4

Bài 2.

a) x² - 9 = x² - 3² = ( x - 3 )( x + 3 )

b) 25 - 4y² = 5² - ( 2y )² = ( 5 - 2y )( 5 + 2y )

c) 9x⁴ - 4y² = ( 3x² )² - ( 2y )² = ( 3x² - 2y )( 3x² + 2y )

d) ( x + 1 )² - y² = ( x - y + 1 )( x + y + 1 )

Answer 2

B1:

a) \(\left(3x+4y\right)^2=\left(3x\right)^2+2.3x.4y+\left(4y\right)^2=9x^2+24xy+16y^2\)

b) \(\left(x^2+1\right)^2=\left(x^2\right)^2+2.x^2.1+1^2=x^4+2x^2+1\)

c) \(\left(3-2y\right)^2=3^2-2.3.2y+\left(2y\right)^2=9-12y+4y^2\)

d) \(\left(xy^2-2\right)^2=\left(xy^2\right)^2-2.xy^2.2+2^2=xy^4-4xy^2+4\)

B2:

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

b) \(25-4y^2=5^2-\left(2y\right)^2=\left(5-2y\right)\left(5+2y\right)\)

c) \(9x^4-4y^2=\left(3x^2\right)^2-\left(2y\right)^2=\left(3x^2-2y\right)\left(3x^2+2y\right)\)

d) \(\left(x+1\right)^2-y^2=\left(x+1-y\right)\left(x+1+y\right)\)

Answer 3

1) Khai triển:
a) (3x + 4y)² = (3x)² + 2.3x.4y + (4y)² = 9x² + 24xy + 16y²
b) (x² + 1)² = (x²)² + 2.x².1 + 1² = x⁴ + 2x²  1
c) (3 - 2y)² = 3² - 2.3.2y + (2y)² = 9 - 12y + 4y²
d) (xy² - 2)² = (xy²)² - 2.xy².2 + 2² = x²y⁴ - 4xy² + 4
2) Viết:
a) x² - 9 = (x - 3)(x + 3)
b) 25 - 4y² = (5 - 2y)(5 + 2y)
c) 9x⁴ - 4y² = (3x² - 2y)(3x² + 2y) 
d) (x + 1)² - y² = (x + 1 - y)(x + 1 + y)