Question

Tính :

a) \(\left(2+xy\right)^2\)

b) \(\left(5-3x\right)^2\)

c) \(\left(5-x^2\right)\left(5+x^2\right)\)

d) \(\left(5x-1\right)^3\)

e) \(\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)

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

Answer 1

Bài giải:

a) (2 + xy)² = 2² + 2 . 2 . xy + (xy)² = 4 + 4xy + x²y²

b) (5 – 3x)²= 5² – 2 . 5 . 3x + (3x)² = 25 – 30x + 9x²

c) (5 – x²)(5 + x²) = 5² – (x²)² = 25 – x⁴

d) (5x – 1)³ = (5x)³ – 3 . (5x)². 1 + 3 . 5x . 1² – 1³ = 125x³ – 75x² + 15x – 1

e) (2x – y)(4x² + 2xy + y²) = (2x – y)[(2x)² + 2x . y + y²] = (2x)³ – y³ = 8x³ – y³

f) (x + 3)(x² – 3x + 9) = (x + 3)(x² – 3x + 3²) = x³ + 3³ = x³ + 27.

Answer 2

a)

\(\left(2+xy\right)^2=\left(4+x^2y^2+4xy\right)\)

b)

\(\left(5-3x\right)^2=25+9x^2-30x\)

c)

\(\left(5-x^2\right)\left(5+x^2\right)=5^2-x^4\)

d)

\(\left(5x-1\right)^3=125x^3-1-75x^2+15x\)

e)

\(\left(2x-y\right)\left(4x^2+2xy+y^2\right)=8x^3-y^3\)

f)

\(\left(x+3\right)\left(x^2-3x+9\right)=x^3+27\)