Ta có: 4x² - y² + 4x + 4y - 3

= (4x² - 4x + 1) - (y² - 4y + 4)

= (2x - 1)² - (y - 2)²

= (2x - 1 -y + 2)(2x - 1 + y - 2)

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

\(4x^2-y^2+4x+4y-3\)

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

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

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

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

Bài làm

( 2x - 1 )( 3 - x ) + ( x + 4 )( x - 3 ) = -3

( x - 3 )( 2x - 1 + x + 4 ) + 3 = 0

( x - 3 )( 3x + 3 ) = 0

=> x - 3 = 0 hoặc 3x - 3 = 0

=> x      = 3 hoặc 3x      = 3

=> x      = 3 hoặc   x      = 3 : 3

=> x      = 3 hoặc   x      = 1

Vậy x = 3; x = 1

# Học tốt #

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

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

\(\Leftrightarrow\left(3-x\right)\left(2x-1-x-4\right)=-3\)

\(\Leftrightarrow\left(3-x\right)\left(x-5\right)=-3\)

\(\Leftrightarrow x^2-8x+15=-3\)

\(\Leftrightarrow x^2-8x+18=0\)

Ta có: \(\Delta=8^2-4.18=-8< 0\)

Vậy pt vô nghiệm

a)A=(x-y)x+y(x-y)=(x-y)(x+y)

Thay x=87,y=13 ta có:(87-13)(87+13)=74×100=7400

b)B=x^2+2x+1-y²=(x+1)²-y²=(x⁺1-y)(x+1+y)

Thay x=94,5,y=4,5 ta có (94,5+1-4,5)(94,5+1+4,5)=91.100=9100

c)C=x^2+1/2x+1/16=(x+1/4)²

^{thay x=49,75 ta có (49,75+1/4)^2=50^2=2500}

Bài 1 : 

a) \(x^4-4x^2-4x-1\)

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

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

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

b) \(x^2+2x-15\)

\(=x^2+2x+1-16\)

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

\(=\left(x+1+4\right)\left(x+1-4\right)=\left(x+5\right)\left(x-3\right)\)

c) \(x^3y-2x^2y^2+5xy\)

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

B2:

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

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

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

\(=-2x^2-4x+11\)

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

\(=\left(x+3-x+3\right)^2=6^2=36\)

c) \(4\left(x-1\right)\left(x+3\right)+5\left(2x+1\right)^2-2\left(5-3x\right)^2\)

\(=4\left(x^2+2x-3\right)+5\left(4x^2+4x+1\right)-2\left(9x^2-30x+25\right)\)

\(=4x^2+8x-12+20x^2+20x+5-18x^2+60x-50\)

\(=6x^2+88x-57\)

Xin lỗi đề là:

   Cho a^3-3ab^2=2 và b^3-3a^2b=-11              CMR: a^2+b^2=5

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

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

\(\Leftrightarrow x^3-3x^2+3x-1+3x^2+3x+3=x^3+8\)

\(\Leftrightarrow x^3+6x+2=x^3+8\)

\(\Leftrightarrow6x=6\Leftrightarrow x=1\)

Nhầm dòng 2

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

\(\Leftrightarrow x^3-3x^2+3x-1+3x^2+6x+3=x^3+8\)

\(\Leftrightarrow x^3+9x+2=x^3+8\)

\(\Leftrightarrow9x=6\)

\(\Leftrightarrow x=\frac{2}{3}\)