Đáp án:
Giải thích các bước giải:
Bài 17 :
a) ( x + y + z + t)( x + y - z - t)
= ( x + y)² - ( z + t)²
= x² + 2xy + y² - ( z² + 2zt + t²)
= x² + 2xy + y² - z² - 2zt - t²
b) ( x - y + z - t)( x - y - z + t)
= ( x - y)² - ( z - t)²
= x² - 2xy + y² - ( z² - 2zt + t²)
= x² - 2xy + y² - z² + 2zt - t²
c) ( x + 2y + 3z + t)³
= [( x + 2y ) + ( 3z + t)]³
= ( x + 2y)³ + 3.(x + 2y)².( 3z + t) + 3.(x + 2y).( 3z + t)² + ( 3z + t)³
= x³ + 6x²y + 12xy² + 8y³ +
(9z + 3t)(x² + 4xy + 4y²) +
(3x + 6y)(9z² + 6zt + t²) + 27z³ + 27z²t + 9zt² + t³
= x³ + 6x²y + 12xy² + 8y³ + 9x²z + 36xyz + 36y²z + 3x²t + 12xyt + 12y²t + 27xz² + 18xzt + 3xt² + 54yz² + 36yzt + 6yt² + 27z³ + 27z²t + 9zt² + t³
= x³ +8y³ + 27z³ + t³ + 6x²y + 12xy² + 36y²z + 3x²t + 27xz² + 3xt² + 54yz² + 6yt² + 27z²t + 9zt² + 36xyz + 12xyt + 18xzt + 36yzt
d) ( x² + 2x - 1)²
= (x²)² +(2x)² + 1² + 2.x².2x - 2.x².1 - 2.2x.1
= x⁴ + 4x² + 1 + 4x³ - 2x² - 4x
= x⁴ + 4x³ + 2x² - 4x + 1
Bài 18 :
a) ( x² - 2x -1)²
= (x²)² + (2x)² + 1² - 2.x².2x - 2.x².1 + 2.2x.1
= x⁴ + 4x² + 1 - 4x³ - 2x² + 4x
= x⁴ - 4x³ + 2x² + 4x +1
b) (m² + 2m - 3)²
= (m²)² + (2m)² + 3² + 2.m².2m -
2.2m.3 - 2.m².3
= m⁴ + 4m² + 9 + 4m³ - 12m - 6m²
= m⁴ + 4m³ - 2m² - 12m + 9
c) (x +1)(x² + 1)(x⁴ + 1)
= 1/(x -1)(x -1)(x +1)(x² +1)(x⁴ + 1)
= 1/(x -1)( x² -1)(x² + 1)( x⁴ + 1)
= 1/(x -1)(x⁴ - 1)( x⁴ + 1)
= 1/(x -1)(x⁸ - 1)
= (x⁸ - 1)/(x -1)
d) 2.( 3 + 1 )( 3² + 1 )( 3⁴ + 1 )
= ( 3 -1)( 3 +1)( 3² + 1)( 3⁴ + 1)
= ( 3² - 1)( 3² + 1)( 3⁴ + 1)
= ( 3⁴ - 1)( 3⁴ + 1)
= 3⁸ - 1
