Tính
a/ ( 2 + xy)^2
c/ ( 5 – x^2)(5 + x^2)
d/ (5x – 1)^3
e/ (2x – y)(4x^2 + 2xy + y^2)
f/ ( x + 3)(x^2 – 3x + 9)
Tính a/ ( 2 + xy)^2 c/ ( 5 – x^2)(5 + x^2) d/ (5x – 1)^3 e/ (2x – y)(4x^2 + 2xy + y^2) f/ ( x + 3)(x^2 – 3x + 9)
By Quinn
By Quinn
Tính
a/ ( 2 + xy)^2
c/ ( 5 – x^2)(5 + x^2)
d/ (5x – 1)^3
e/ (2x – y)(4x^2 + 2xy + y^2)
f/ ( x + 3)(x^2 – 3x + 9)
Đáp án:
a/ ( 2 + xy )² = 2² + 2 . 2 . xy + (xy)² = 4 + 4xy + x²y²
c/ ( 5 – x² )( 5 + x² ) = 5² – ( x² ) ² = 5² – $x^{4}$
d/ ( 5x – 1 )³ = ( 5x )³ – 3 . ( 5x ) ² + 3 . 5x . 1² – 1³ = 125x³ – 75x² + 15x – 1
e/ ( 2x – y )( 4x² + 2xy + y²) = ( 2x )³ – y³ = 8x³ – y³
f/ ( x + 3 )( x² – 3x + 9 ) = x³ + 3³ = x³ + 27
Giải thích các bước giải:
`a) (2 + xy)^2 `
`= 2^2 + 2 . 2 . xy + (xy)^2`
`= 4 + 4xy + x^2y^2`
`c) (5 – x^2)(5 + x^2)`
`= 5^2 – (x^2)^2`
`= 25 – x^4`
`d) (5x – 1)^3 `
`= (5x)^3 – 3.(5x)^2 . 1 + 3 . 5x . 1^2 – 1^3`
`= 125x^3 – 75x^2 + 15x – 1`
`e) (2x – y)(4x^2 + 2xy + y^2)`
`= (2x)^3 – y^3`
`= 8x^3 – y^3`
`f) (x +3)(x^2 – 3x + 9)`
`= x^3 + 3^3`
`= x^3 + 27`