3(x - 1)² - (x + 1)³

= 3(x² - 2x + 1) - (x³ + 2x² + 2x + 1)

= 3x² - 6x + 3 - x³ - 2x² - 2x - 1

= 3x² - 2x² - 6x - 2x - x³ + 3 - 1

= x² - 8x - x³ + 2

\(a,=x^3+3x^2+3x+1\\ b,=8x^3+36x^2+54x+27\\ c,=x^3+\dfrac{3}{2}x^2+\dfrac{3}{4}x+\dfrac{1}{8}\\ d,=x^6-6x^4+12x^2-8\\ e,=8x^3-36x^2y+54xy^2-27y^3\)

a.(x+3)(x+1)

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

=x²+x+3x+3

=x²+4x+3

b.(x+6)(2x-2)

=x.(2x-2)+6.(2x-2)

=2x²-2x+12x-12

=2x²+10x-12

c) \(\left(2\sqrt{x}+1\right)^2=4x+4\sqrt{x}+1\)

a) \(\left(\dfrac{1}{2}m+3\right)^3=\dfrac{m^3}{8}+\dfrac{9m^2}{4}+\dfrac{27m}{2}+9\)

b) \(2\left(m+\dfrac{1}{2}\right)=2m+1\)

c) \(\left(2\sqrt{x}+1\right)^2=4x+4\sqrt{x}+1\)

d) \(\left(2\sqrt{2}+\dfrac{1}{4}\right)^2=8+\sqrt{2}+\dfrac{1}{16}=\dfrac{129}{16}+\sqrt{2}\)

chi tiết câu c

c) \(\left(2\sqrt{x}+1\right)^2=\left(2\sqrt{x}\right)^2+2\cdot2\sqrt{x}\cdot1+1^2=4x+4\sqrt{x}+1\)

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

\(=3x^3-15x^2+9x+x^2+2x+x+2\)

\(=3x^3-14x^2+13x+2\)

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

\(=3x^3-15x^2+9x+\left(x^2+2x+x+2\right)\)

\(=3x^3-15x^2+9x+x^2+2x+x+2\)

\(=3x^3-14x^2+13x+2\)

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

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

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

\(=x^2-2x+14x\)

Câu 7:

a: \(A=x^2-2x+7\)

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

\(=\left(x-1\right)^2+6\ge6\forall x\)

Dấu '=' xảy ra khi x-1=0

=>x=1

b: \(B=5x^2-20x\)

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

\(=5\left(x^2-4x+4-4\right)=5\left(x-2\right)^2-20\ge-20\forall x\)

Dấu '=' xảy ra khi x-2=0

=>x=2

Câu 4:

a: \(A=\left(x-y\right)^2+\left(x+y\right)^2\)

\(=x^2-2xy+y^2+x^2+2xy+y^2\)

\(=2x^2+2y^2\)

b: \(B=\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)

\(=4x^2-4x+1-2\left(4x^2-12x+9\right)+4\)

\(=4x^2-4x+5-8x^2+24x-18=-4x^2+20x-13\)

Câu 2:

a: \(x^2-4x+4=x^2-2\cdot x\cdot2+2^2=\left(x-2\right)^2\)

b: \(x^2+10x+25=x^2+2\cdot x\cdot5+5^2=\left(x+5\right)^2\)

c: \(\frac{x^2}{4}-x+1=\left(\frac12x\right)^2-2\cdot\frac12x\cdot1+1^2=\left(\frac12x-1\right)^2\)

d: \(9\left(x+1\right)^2-6\left(x+1\right)+1\)

\(=\left(3x+3\right)^2-2\cdot\left(3x+3\right)\cdot1+1^2\)

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

e: \(\left(x-2y\right)^2-8\left(x^2-2xy\right)+16x^2\)

\(=\left(x-2y\right)^2-2\cdot\left(x-2y\right)\cdot4x+\left(4x\right)^2\)

\(=\left(x-2y-4x\right)^2=\left(-3x-2y\right)^2\)

a. (x + y)² = x² + 2xy + y²

b. (x - 2y)² = x² - 4xy - 4x²

c. (xy² + 1)(xy² - 1) = x²y⁴ - 1

d. (x + y)²(x - y)² = (x² + 2xy + y²)(x² - 2xy + y²) = x⁴ - (2xy + y²)² = x⁴ - (4x²y² + y⁴) = x⁴ - 4x²y² - y⁴

^{Chucs hocj toots}

Câu 2: 

a: \(x^2-4x+4=\left(x-2\right)^2\)

b: \(x^2+10x+25=\left(x+5\right)^2\)

d: \(9\left(x+1\right)^2-6\left(x+1\right)+1=\left(3x+2\right)^2\)

e: \(\left(x-2y\right)^2-8\left(x-2xy\right)+16x^2=\left(x-2y+4x\right)^2=\left(5x-2y\right)^2\)

\(\left(2-3x\right)^3=8-36x+54x^2-27x^3\)

\(\left(3-2x\right)^2=9-12x+4x^2\)