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Trả lời:

Bài 4:

b, B =  ( x + 1 ) ( x⁷ - x⁶ + x⁵ - x⁴ + x³ - x² + x - 1 ) 

= x⁸ - x⁷ + x⁶ - x⁵ + x⁴ - x³ + x² - x + x⁷ - x⁶ + x⁵ - x⁴ + x³ - x² + x - 1 

= x⁸ - 1

Thay x = 2 vào biểu thức B, ta có:

2⁸ - 1 = 255

c, C = ( x + 1 ) ( x⁶ - x⁵ + x⁴ - x³ + x² - x + 1 ) 

= x⁷ - x⁶ + x⁵ - x⁴ + x³ - x² + x + x⁶ - x⁵ + x⁴ - x³ + x² - x + 1

= x⁷ + 1

Thay x = 2 vào biểu thức C, ta có:

2⁷ + 1 = 129

d, D = 2x ( 10x² - 5x - 2 ) - 5x ( 4x² - 2x - 1 ) 

= 20x³ - 10x² - 4x - 20x³ + 10x² + 5x

= x

Thay x = - 5 vào biểu thức D, ta có:

D = - 5

Bài 5: 

a, A = ( x³ - x²y + xy² - y³ ) ( x + y )

= x⁴ + x³y - x³y - x²y² + x²y² + xy³ - xy³ - y⁴

= x⁴ - y⁴

Thay x = 2; y = - 1/2 vào biểu thức A, ta có:

A = 2⁴ - ( - 1/2 )⁴ = 16 - 1/16 = 255/16

b, B = ( a - b ) ( a⁴ + a³b + a²b² + ab³ + b⁴ ) 

= a⁵ + a⁴b + a³b² + a²b³ + ab⁴ - ab⁴ - a³b² - a²b³ - ab⁴ - b⁵ 

= a⁵ + a⁴b - ab⁴ - b⁵

Thay a = 3; b = - 2 vào biểu thức B, ta có:

B = 3⁵ + 3⁴.( - 2 ) - 3.( - 2 )⁴ - ( - 2 )⁵ = 243 - 162 - 48 + 32 = 65

c, ( x² - 2xy + 2y² ) ( x² + y² ) + 2x³y - 3x²y² + 2xy³ 

= x⁴ + x²y² - 2x³y - 2xy³ + 2x²y² + 2y⁴ + 2x³y - 3x²y² + 2xy³

= x⁴ + 2y⁴

Thay x = - 1/2; y = - 1/2 vào biểu thức trên, ta có:

( - 1/2 )⁴ + 2.( - 1/2 )⁴ = 1/16 + 2. 1/16 = 1/16 + 1/8 = 3/16

Bài 1: 

a) \(-5\left(x^2-3x+1\right)+x\left(1+5x\right)=x-2\)

\(\Rightarrow-5x^2+15x-5+x+5x^2=x-2\)

\(\Rightarrow16x-5=x-2\)

\(\Rightarrow16x-x=5-2\)

\(\Rightarrow15x=3\)

\(\Rightarrow x=\dfrac{15}{3}=5\)

b) \(12x^2-4x\left(3x+5\right)=10x-17\)

\(\Rightarrow12x^2-12x^2-20x=10x-17\)

\(\Rightarrow-20x=10x-17\)

\(\Rightarrow-20x-10x=-17\)

\(\Rightarrow-30x=-17\)

\(\Rightarrow x=\dfrac{-30}{-17}=\dfrac{30}{17}\)

c) \(-4x\left(x-5\right)+7x\left(x-4\right)-3x^2=12\)

\(\Rightarrow-4x^2+20x+7x^2-28x-3x^2=12\)

\(\Rightarrow-8x=12\)

\(\Rightarrow x=\dfrac{12}{-8}=-\dfrac{4}{3}\)

Bài 2: 

a) \(\left(x+5\right)\left(x-7\right)-7x\left(x-3\right)\)

\(=x^2-7x+5x-35-7x^2+21x\)

\(=-6x^2+19x-35\)

b) \(x\left(x^2-x-2\right)-\left(x-5\right)\left(x+1\right)\)

\(=x^3-x^2-2x-x^2+x-5x-5\)

\(=x^3-2x^2-6x-5\)

c) \(\left(x-5\right)\left(x-7\right)-\left(x+4\right)\left(x-3\right)\)

\(=x^2-7x-5x+35-x^2-3x+4x-12\)

\(=11x+23\)

d) \(\left(x-1\right)\left(x-2\right)-\left(x+5\right)\left(x+2\right)\)

\(=x^2-2x-x+2-x^2+2x+5x+10\)

\(=4x+12\)

bài 1:

a) (x+1)^2-(x-1)^2-3(x+1)(x-1)

=(x+1+x-1)(x+1-x+1)-3x^2-3

=2x^2-3x^2-3

=-x^2-3

Bài 1.

a) 2x² + 3( x - 1 )( x + 1 ) - 5x( x + 1 )

= 2x² + 3( x² - 1 ) - 5x² - 5x

= 2x² + 3x² - 3 - 5x² - 5x

= -5x - 3 

b) 4( x - 1 )( x + 5 ) - ( x - 2 )( x + 5 ) - 3( x - 1 )( x + 2 )

= 4( x² + 4x - 5 ) - ( x² + 3x - 10 ) - 3( x² + x - 2 )

= 4x² + 16x - 20 - x² - 3x + 10 - 3x² - 3x + 6

= 10x - 4

Bài 2.

a) ( 8 - 5x )( x + 2 ) + 4( x - 2 )( x + 1 ) + 2( x - 2 )( x + 2 ) = 0

<=> -5x² - 2x + 16 + 4( x² - x - 2 ) + 2( x² - 4 ) = 0

<=> -5x² - 2x + 16 + 4x² - 4x - 8 + 2x² - 8 = 0

<=> x² - 6x = 0

<=> x( x - 6 ) = 0

<=> x = 0 hoặc x = 6

b) ( x + 3 )( x + 2 ) - ( x - 2 )( x + 5 ) = 0

<=> x² + 5x + 6 - ( x² + 3x - 10 ) = 0

<=> x² + 5x + 6 - x² - 3x + 10 = 0

<=> 2x + 16 = 0

<=> 2x = -16

<=> x = -8

Bài 3.

A = ( n² + 3n - 1 )( n + 2 ) - n³ + 2

= n³ + 2n² + 3n² + 6n - n - 2 - n³ + 2

= 5n² + 5n

= 5n( n + 1 ) chia hết cho 5 ( đpcm )

B = ( 6n + 1 )( n + 5 ) - ( 3n + 5 )( 2n - 1 )

= 6n² + 30n + n + 5 - ( 6n² - 3n + 10n - 5 )

= 6n² + 31n + 5 - 6n² - 7n + 5

= 24n + 10

= 2( 12n + 5 ) chia hết cho 2 ( đpcm )

bài 1:a,\(2x^2+3\left(x-1\right)\left(x+1\right)-5x\left(x+1\right)\)

\(=2x^2+3x^2-3-5x^2-5x\)

\(=-3-5x\)

b.\(4\left(x-1\right)\left(x+5\right)-\left(x-2\right)\left(x+5\right)-3\left(x-1\right)\left(x+2\right)\)

\(=4\left(x^2+4x-5\right)-\left(x^2+3x-10\right)-3\left(x^2+x-2\right)\)

\(=4x^2+16x-20-x^2-3x+10-3x^2-3x+6\)

\(=10x-4\)

\(\left(8-5x\right)\left(x+2\right)+4\left(x-2\right)\left(x+1\right)+2\left(x-2\right)\left(x+2\right)=0\)

\(8x+16-5x^2-10x+4\left(x^2+x-2x-2\right)+2\left(x^2+2x-2x-4\right)=0\)

\(-2x+16-5x^2+4x^2-4x-8+2x^2-8=0\)

\(x^2-6x=0\)

\(x\left(x-6\right)=0\)

\(\orbr{\begin{cases}x=0\\x-6=0\end{cases}\Rightarrow\orbr{\begin{cases}x=0\\x=6\end{cases}}}\)

Bài 1

a) 3 2/5 - 1/2

= 17/5 - 1/2

= 34/10 - 5/10

= 29/10

b) 4/5 + 1/5 × 3/4

= 4/5 + 3/20

= 16/20 + 3/20

= 19/20

c) 3 1/2 × 1 1/7

= 7/2 × 8/7

= 4

d) 4 1/6 : 2 1/3

= 25/6 : 7/3

= 25/14

Bài 2

a) 3 × 1/2 + 1/4 × 1/3

= 3/2 + 1/12

= 18/12 + 1/12

= 19/12

b) 1 4/5 - 2/3 : 2 1/3

= 9/5 - 2/3 : 7/3

= 9/5 - 2/7

= 63/35 - 10/35

= 53/35

Bài 1

a) 3 2/5 - 1/2

= 17/5 - 1/2

= 34/10 - 5/10

= 29/10

b) 4/5 + 1/5 × 3/4

= 4/5 + 3/20

= 16/20 + 3/20

= 19/20

c) 3 1/2 × 1 1/7

= 7/2 × 8/7

= 4

d) 4 1/6 : 2 1/3

= 25/6 : 7/3

= 25/14

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