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

= - 3x^2 +4x -1

b) =5x^2 + 10x - 10x - 20 - 1/2 .(36 - 96x + 64x^2 ) +17

= 5x^2 - 20 - 18 - 48 x - 32x^2 +17

= -27x^2 - 48x - 3

Chúc bn hok tốt a !

\(5\left(x+2\right)\left(x-2\right)-\frac{1}{2}\left(6-8x\right)^2+17\)

\(=5\left(x^2-4\right)-\frac{1}{2}\left(36-96x+64x^2\right)+17\)

\(=5x^2-20+30-32x^2+17=-27x^2+27\)

\(\left(x^2-1^3\right)-\left(x^4+x^2+1\right)\left(x^2-1\right)\)

\(=x^2-1-\left(x^6-x^4+x^4-x^2+x^2-1\right)\)

\(=x^2-1-x^6+1=x^2-x^6\)

1. 5( x + 2 )( x - 2 ) - 1/2( 6 - 8x )² + 17

= 5( x² - 4 ) - 1/2( 36 - 96x + 64x² ) + 17

= 5x² - 20 - 18 + 48x - 32x² + 17

= -27x² + 48x - 21

2. ( x² - 1³ ) - ( x⁴ + x² + 1 )( x² - 1 )

= ( x² - 1 ) - ( x⁴ + x² + 1 )( x² - 1 )

= ( x² - 1 )[ 1 - ( x⁴ + x² + 1 ) ]

= ( x² - 1 )( 1 - x⁴ - x² - 1 )

= ( x² - 1 )( -x⁴ - x² )

= -x⁶ - x⁴ + x⁴ + x²

= x² - x⁶

a: \(\left(2x+1\right)^2+2\left(4x^2-1\right)+\left(2x-1\right)^2\)

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

\(=\left(2x+1+2x-1\right)^2=\left(4x\right)^2=16x^2\)

b: \(\left(x^2-1\right)\left(x+2\right)-\left(x-2\right)\left(x^2+2x+4\right)\)

\(=x^3+2x^2-x-2-x^3+8\)

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

a) \(\left(2x+1\right)^2+2\left(4x^2-1\right)+\left(2x-1\right)^2\)

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

\(=\left[\left(2x+1\right)+\left(2x-1\right)\right]^2\)

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

\(=\left(4x\right)^2\)

\(=16x^2\)

b) \(\left(x^2-1\right)\left(x+2\right)-\left(x-2\right)\left(x^2+2x+4\right)\)

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

\(=x^3+2x^2-x-2-x^3+8\)

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

\(a,\left(2x+1\right)^2+2\left(4x^2-1\right)+\left(2x-1\right)^2\)

\(=\left(2x+1\right)^2+2\cdot\left[\left(2x\right)^2-1^2\right]+\left(2x-1\right)^2\)

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

\(=\left[\left(2x+1\right)+\left(2x-1\right)\right]^2\)

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

\(=\left(4x\right)^2\)

\(=16x^2\)

\(---\)

\(b,\left(x^2-1\right)\left(x+2\right)-\left(x-2\right)\left(x^2+2x+4\right)\)

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

\(=x^3+2x^2-x-2-x^3+8\)

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

a: \(2x\left(2x-1\right)^2-3x\left(x+3\right)\left(x-3\right)-4x\left(x+1\right)^2\)

\(=2x\left(4x^2-4x+1\right)-3x\left(x^2-9\right)-4x\left(x^2+2x+1\right)\)

\(=8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x\)

\(=x^3-16x^2+25x\)

a: \(A=\dfrac{1}{x-1}\cdot5\sqrt{3}\cdot\left|x-1\right|\cdot\sqrt{x-1}\)

\(=\dfrac{5\sqrt{3}}{x-1}\cdot\left(x-1\right)\cdot\sqrt{x-1}=5\sqrt{3}\cdot\sqrt{x-1}\)

b: \(B=10\sqrt{x}-3\cdot\dfrac{10\sqrt{x}}{3}-\dfrac{4}{x}\cdot\dfrac{x\sqrt{x}}{2}\)

\(=10\sqrt{x}-10\sqrt{x}-\dfrac{4\sqrt{x}}{2}=-2\sqrt{x}\)

c: \(C=x-4+\left|x-4\right|\)

=x-4+x-4

=2x-8

b, 5(x + 2) (x - 2 ) - 1/2 (6-8x)² + 17

=5x +10 (x - 2) - 1/2 . 6 - 1/2 . 8x +17

=5x + 10x - 20 - 3 - 4x +17

=15x - 17 -4x + 17 

=15x - 4x -17 + 17

=11x - 0 =11x

a, (x+1)² - (x-1)² - 3(x+1) (x-1)

=(x+1)+(x-1).(x+1)-(x-1) - 3x+3x -3

=2x.0 - 3x

=-3x

a

(x+1)-(x-1)-3(x+1)(x-1)

=(x+1)-(x-1)-3x+1.(x-1)

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

=x+1-x+1-3x+x-1

=x-x-3x+x+1+1-1

=-2x

b,

5(x+2)(x-2)-1/2(6-8x)^2+17

=5x+10(x-2)-1/2(36-64x²)+17

=5x+10x-20-18+32x²+17

=5x+10x-20-18+17+32x²

=15x-21+32x²

a

(x+1)-(x-1)-3(x+1)(x-1)

=(x+1)-(x-1)-3x+1.(x-1)

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

=x+1-x+1-3x+x-1

=x-x-3x+x+1+1-1

=-2x

b,

5(x+2)(x-2)-1/2(6-8x)^2+17

=5x+10(x-2)-1/2(36-64x²)+17

=5x+10x-20-18+32x²+17

=5x+10x-20-18+17+32x²

=15x-21+32x²

a

(x+1)-(x-1)-3(x+1)(x-1)

=(x+1)-(x-1)-3x+1.(x-1)

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

=x+1-x+1-3x+x-1

=x-x-3x+x+1+1-1

=-2x

b,

5(x+2)(x-2)-1/2(6-8x)^2+17

=5x+10(x-2)-1/2(36-64x²)+17

=5x+10x-20-18+32x²+17

=5x+10x-20-18+17+32x²

=15x-21+32x²

a: \(\left(x-2y\right)^2+\left(x-\dfrac{1}{2}y\right)\left(x+\dfrac{1}{2}y\right)\)

\(=x^2-4xy+4y^2+x^2-\dfrac{1}{4}y^2\)

\(=2x^2-4xy+\dfrac{15}{4}y^2\)

b: \(\left(x-2\right)^2+\left(x+3\right)^2-2\left(x-1\right)\left(x+1\right)\)

\(=x^2-4x+4+x^2+6x+9-2\left(x^2-1\right)\)

\(=2x^2+2x+13-2x^2+2\)

=2x+15

a) \(=x^2-4xy+4y^2+x^2-\dfrac{1}{4}y^2=2x^2-4xy+\dfrac{15}{4}y^2\)

b) \(=x^2-4x+4+x^2+6x+9-2x^2+2\)

\(=2x+15\)

a; \(\left(x-2y\right)^2+\left(x-\dfrac{1}{2}y\right)\left(x+\dfrac{1}{2}y\right)\)

= \(x^2-4xy+4y^2+x^2-\dfrac{1}{4}y^2\)

= \(2x^2-4xy+\dfrac{15}{4}y^2\)

b; \(\left(x-2\right)^2+\left(x+3\right)^2-2\left(x-1\right)\left(x+1\right)\)

= \(x^2-4x+4+x^2+6x+9-2x^2+2\)

= \(2x+15\)