Bài 4:Rút gọn biểu thức
a) \(2x\left(x-5\right)-\left(x-2\right)^2-\left(x+3\right).\left(x-3\right)\)
b) \(\left(x+1\right)^2+3\left(x-5\right).\left(x+5\right)-\left(2x-1\right)^2\)
c) \(2x\left(x-7\right)-\left(x+3\right)\left(x-2\right)-\left(x+4\right)\left(x-4\right)\)
d) \(\left(x+3\right)\left(x-3\right)-\left(x+5\right).\left(x-1\right)-\left(x-4\right)^2\)
a. \(2x\left(x-5\right)-\left(x-2\right)^2-\left(x+3\right)\left(x-3\right)\)
\(=2x^2-10x-x^2+4x-4-x^2+9\)
\(=-6x+5\)
b. \(\left(x+1\right)^2+3\left(x-5\right)\left(x+5\right)-\left(2x-1\right)^2\)
\(=x^2+2x+1+3x^2-75-4x^2+4x-1\)
\(=6x-75\)
c. \(2x\left(x-7\right)-\left(x+3\right)\left(x-2\right)-\left(x+4\right)\left(x-4\right)\)
\(=2x^2-14x-x^2-x+6-x^2+16\)
\(=-15x+22\)
d. \(\left(x+3\right)\left(x-3\right)-\left(x+5\right)\left(x-1\right)-\left(x-4\right)^2\)
\(=x^2-9-x^2-4x+5-x^2+8x-16\)
\(=-x^2+4x-20\)
Bài làm:
a) \(2x\left(x-5\right)-\left(x-2\right)^2-\left(x+3\right)\left(x-3\right)\)
\(=2x^2-10x-x^2+4x-4-x^2+9\)
\(=-6x+5\)
b) \(\left(x+1\right)^2+3\left(x-5\right)\left(x+5\right)-\left(2x-1\right)^2\)
\(=x^2+2x+1+3x^2-75-4x^2+4x-1\)
\(=6x-75\)
c) \(2x\left(x-7\right)-\left(x+3\right)\left(x-2\right)-\left(x+4\right)\left(x-4\right)\)
\(=2x^2-14x-x^2-x+6-x^2+16\)
\(=-15x+22\)
d) \(\left(x+3\right)\left(x-3\right)-\left(x+5\right)\left(x-1\right)-\left(x-4\right)^2\)
\(=x^2-9-x^2-4x+5-x^2+8x-16\)
\(=-x^2-4x-20\)
đầy đủ từng bước nhé
\(a,2x\left(x-5\right)-\left(x-2\right)^2-\left(x+3\right)\left(x-3\right)\)
\(=2x^2-10x-\left(x^2-4x+4\right)-\left(x^2-9\right)\)
\(=2x^2-10x-x^2+4x-4-x^2+9\)
\(=\left(2x^2-x^2-x^2\right)+\left(4x-10x\right)+\left(9-4\right)\)
\(=0-6x+5=5-6x\)
\(b,\left(x+1\right)^2+3\left(x-5\right)\left(x+5\right)-\left(2x-1\right)^2\)
\(=\left(x^2+2x+1\right)+3\left(x^2-25\right)-\left(4x^2-4x+1\right)\)
\(=x^2+2x+1+3x^2-75-4x^2+4x-1\)
\(=\left(x^2+3x^2-4x^2\right)+\left(2x+4x\right)+\left(1-1-75\right)\)\(=6x-75\)
\(c,2x\left(x-7\right)-\left(x+3\right)\left(x-2\right)-\left(x+4\right)\left(x-4\right)\)
\(=2x^2-14x-\left(x+2\right)\left(x-2\right)-x+2-\left(x+4\right)\left(x-4\right)\)
\(=2x^2-14x-x^2+4-x+2-x^2+16\)
\(=\left(2x^2-x^2-x^2\right)+\left(-14x-x\right)+\left(16+2+4\right)\)
\(=0-15x+22=22-15x\)
\(d,\left(x+3\right)\left(x-3\right)-\left(x+5\right)\left(x-1\right)-\left(x-4\right)^2\)
\(=\left(x+3\right)\left(x-3\right)-\left(x+1\right)\left(x-1\right)-4\left(x-1\right)-\left(x-4\right)^2\)
\(=x^2-9-x^2+1-4x+4-\left(x^2-8x+16\right)\)
\(=\left(x^2-x^2\right)-4x+\left(4+1-9\right)-x^2+8x-16\)
\(=-4x-4-x^2+8x-16=-x^2+\left(8x-4x\right)-\left(16+4\right)\)
\(=-x^2+4x-20\)
a) 2x( x - 5 ) - ( x - 2 )2 - ( x + 3 )( x - 3 )
= 2x2 - 10x - ( x2 - 4x + 4 ) - ( x2 - 9 )
= 2x2 - 10x - x2 + 4x - 4 - x2 + 9
= -6x + 5
b) ( x + 1 )2 + 3( x - 5 )( x + 5 ) - ( 2x - 1 )2
= x2 + 2x + 1 + 3( x2 - 25 ) - ( 4x2 - 4x + 1 )
= x2 + 2x + 1 + 3x2 - 75 - 4x2 + 4x - 1
= 6x - 75
c) 2x( x - 7 ) - ( x + 3 )( x - 2 ) - ( x + 4 )( x - 4 )
= 2x2 - 14x - ( x2 + x - 6 ) - ( x2 - 16 )
= 2x2 - 14x - x2 - x + 6 - x2 + 16
= -15x + 22
d) ( x + 3 )( x - 3 ) - ( x + 5 )( x - 1 ) - ( x - 4 )2
= x2 - 9 - ( x2 + 4x - 5 ) - ( x2 - 8x + 16 )
= x2 - 9 - x2 - 4x + 5 - x2 + 8x - 16
= -x2 + 4x - 20
a, \(\left(x+1\right)^2+3\left(x-5\right)\left(x+5\right)-\left(2x-1\right)^2\)
\(=x^2+2x+1+3\left(x^2-25\right)-\left(4x^2-2x+1\right)\)
\(=x^2+2x+1+3x^2-75-4x^2+4x-1\)
\(=6x-75\)
b, \(\left(x+3\right)\left(x-3\right)-\left(x+5\right)\left(x-1\right)-\left(x-4\right)^2\)
\(=x^2-3x+3x-9-\left(x^2-x+5x-5\right)-\left(x^2-8x+16\right)\)
\(=x^2-9-x^2-4x+5-x^2+8x-16\)
\(=-x^2-20+4x\)
