a) (x+3)(x^2-3x+9)-(54+x^3)

= x^3- 3x^2+9x+3x^2-9x+27-54-x63

= -27

b) (2x + y)(4x^2 – 2xy + y^2) – (2x – y)(4x^2+ 2xy + y^2)

= (2x + y)[(2x)^2 – 2x.y + y^2] – (2x – y)[(2x)^2 + 2x.y + y^2]

= [(2x)3^3+ y^3] – [(2x)^3 – y^3]

= (2x)^3 + y^3 – (2x)^3 + y^3

= 2y^3

a)(x+3)(X^2-3x+9)-(54+x^3)

= \(x^3\)+ \(3^3 \) - 54 -\(x^3\)

= 27- 54

= -27

b)(2x+y)(4x^2-2xy+y^2)-(2x-y)(4x^2+2xy+y^2)

= \((2x)^3\) + \(y^3\)  - [\((2x)^3\) - \(y^3\) ]

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

= \(2y^3\)

a) Ta có: \(\left(x+3\right)\left(x^2-3x+9\right)-\left(54+x^3\right)\)

\(=x^3+27-54-x^3\)

=-27

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

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

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

\(=\left(2x+y\right)\left(8x^2+2y^2\right)\)

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

a: \(=8x^3+y^3-8x^3+y^3=2y^3\)

b: \(=25-x^4\)

c: \(=a^2+2ab+b^2-a^2+2ab-b^2=4ab\)

d: \(=a^3+3a^2b+3ab^2+b^3-a^3+3a^2b-3ab^2+b^3-2b^2\)

\(=6a^2b+2b^3-2b^2\)

e: \(=\left(x-1\right)^3\)

Bài 2: 

a) Ta có: \(A=\left(7x+5\right)^2+\left(3x-5\right)^2-\left(10-6x\right)\left(5+7x\right)\)

\(=\left(7x+5\right)^2+2\cdot\left(7x+5\right)\cdot\left(3x-5\right)+\left(3x-5\right)^2\)

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

\(=\left(10x\right)^2=100x^2\)

Thay x=-2 vào A, ta được:

\(A=100\cdot\left(-2\right)^2=100\cdot4=400\)

b) Ta có: \(B=\left(2x+y\right)\left(y^2-2xy+4x^2\right)-8x\left(x-1\right)\left(x+1\right)\)

\(=8x^3+y^3-8x\left(x^2-1\right)\)

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

\(=8x+y^3\)

Thay x=-2 và y=3 vào B, ta được:

\(B=-2\cdot8+3^3=-16+27=11\)

Ai help mk vs

Bài 1: 

Ta có: \(A=x\left(4-x\right)\)

\(=4x-x^2\)

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

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

\(=-\left(x-2\right)^2+4\le4\forall x\)

Dấu '=' xảy ra khi x=2

Vậy: \(A_{max}=4\) khi x=2

Trả lời:

a, ( 2x + y )³ - ( 2x - y )³ 

= ( 2x )³ + 3.( 2x )².y + 3.2x.y² + y³ - [ ( 2x )³ - 3.( 2x )².y + 3.2x.y² - y³ ] 

= 8x³ + 12x²y + 6xy² + y³ - ( 8x³ - 12x²y + 6xy² - y³ )

= 8x³ + 12x²y + 6xy² + y³ - 8x³ + 12x²y - 6xy² + y³

= 24x²y + 2y³

b, ( 5 - 3x )³ - ( 5 + 3x )³ 

= 5³ - 3.5².3x + 3.5.( 3x )² - ( 3x )³ - [ 5³ + 3.5².3x + 3.5.( 3x )² + ( 3x )³ ]

= 125 - 225x + 135x² - 27x³ - ( 125 + 225x + 135x² + 27x³ )

= 125 - 225x + 135x² - 27x³ - 125 - 225x - 135x² - 27x³

=  - 54x³- 450x​

c, ( x + 3 ) ( x² - 2x + 9 ) - ( 54 + x³ )

= x³ - 2x² + 9x + 3x² - 6x + 27 - 54 - x³

= x² + 3x - 27

d, ( 2x + y ) ( 4x² - 2xy + y² ) - 2xy ( 4x² + 2xy + y² )

= ( 2x )³ + y³ - 8x³y - 4x²y² - 2xy³ 

= 8x³ + y³ - 8x³y - 4x²y² - 2xy³

a ) \(\left(x+3\right)\left(x^2-3x+9\right)-\left(5x+x^3\right)\)

\(=\left(x+3\right)\left(x^2-3x+3^2\right)-\left(54+x^3\right)\)

\(=x^3+3^3-\left(54+x^3\right)\)

\(=x^3+27-54-x^3\)

\(=-27\)

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

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

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

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

\(=2y^3\)

a )

b )

câu c (x+3)(x^2-3x+9)-(54+x^3)=x^3+27-54-x^3

=27

A= (6x-2)^2 + (2-5x)^2+2(6x-2)(2-5x)

= (6x-2)^2 +2(6x-2)(2-5x)+ (2-5x)^2

\(=\left(6x-2+2-5x\right)^2=x^2\)

B= (2a^2+2a+1)(2a^2-2a+1)-(2a^2+1)^2

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

C=(x+3)(x^2-3x+9)-(54+x^3)

\(=\left(x^3+27\right)-54-x^3=27\)

D=(2x+y)(4x^2-2xy+y^2)-(2x-y)(4x^2+2xy+y^2)

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

E=(a+b)^2-(a-b)^2

\(=\left(a+b+a-b\right)\left(a+b-a+b\right)=2a.2b=4ab\)

Secret Personv: thật.CTV lạ z

\(C=\left(x+3\right)\left(x^2-3x+9\right)-\left(54+x^3\right)\)

\(=x^3-27-54-x^3=-81\)

\(C=\left(x+3\right)\left(x^2-3x+9\right)-\left(54+x^3\right)\)

\(=x^3+27-54-x^3=-27\)