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(x - 1)(x + 1)(x2 + 1)
Áp dụng HĐT số 3 : (A + B)(A - B) = A2 - B2
= (x2 - 12)(x2 + 1) = (x2 - 1)(x2 + 1) = (x2)2 - 12 = x4 - 1
a, \(3\left(2x+1\right)^2-2\left(x-5\right)^2+\left(x-1\right)\left(x+2\right)\)
\(=3\left(4x^2+4x+1\right)-2\left(x^2-10x+25\right)+x^2+x-2\)
\(=12x^2+12x+3-2x^2+20x-50+x^2+x-2\)
\(=11x^2+33x-49\)
\(3\left(2x+1\right)^2-2\left(x-5\right)^2+\left(x-1\right)\left(x+2\right)\)
\(=3\left(4x^2+4x+1\right)-2\left(x^2-10x+10\right)+x^2+2x-x-2\)
\(=12x^2+12x+3-2x^2-20x-20+x^2+2x-x-2\)
\(=11x^2+33x-15\)
a) \(\left(2x^2-3x\right)\left(5x^2-2x+1\right)\)
\(=10x^4-4x^3+2x^2-15x^3+6x^2-3x\)
\(=10x^4-19x^3+8x^2-3x\)
b) \(\left(x+1\right)\left(x^2-x+1\right)-x\left(x+3\right)\left(x+5\right)\)
\(=x^3+1-x\left(x^2+8x+15\right)\)
\(=x^3+1-x^3-8x^2-15x\)
\(=-8x^2-15x+1\)
(2x - 1)(x2 - 2xy + 3y2) = \(2x^3-4x^2y+6xy^2-x^2+2xy-3y^2\)
a) 3(x + 1) - 3x = 3x + 3 - 3x = (3x - 3x) + 3 = 3
b) x3 - x(x2 - 2) = x3 - x3 + 2x = (x3 - x3) + 2x = 2x
Bài làm:
a) \(3\left(x+1\right)-3x\)
\(=3x+3-3x\)
\(=3\)
b) \(x^3-x\left(x^2-2\right)\)
\(=x^3-x^3+2x\)
\(=2x\)
\(\left(x^2-2x\right)\left(3x^2-x+1\right)\)
\(=3x^4-x^3+x^2-6x^3+2x^2-2x\)
\(=3x^4-7x^3+3x^2-2x\)
=.= hok tốt!!
\(\left(x^2-2x\right)\times\left(3x^2-x+1\right)\)
\(=3x^4-x^3+x^2-6x^3+2x^2-2x\)
\(=3x^4-9x^3+3x^2-2x\)
`@` `\text {Ans}`
`\downarrow`
`x(1-x) + (x-1)^2`
`= x-x^2 + x^2 - 2x + 1`
`= (x-2x) + (-x^2 + x^2) + 1`
`= -x+1`
x ( 1 - x ) + ( x - 1 )2 = x - x2 + x2 - 2x + 1 = -x + 1 = 1 - x