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a) 4x2(5x3 - 2x + 3)
= (4x2 . 5x3) - (4x2 . 2x) + (4x2 . 3)
= 20x5 - 8x3 + 12x2
b) (-5x3)(2x2 + 3x - 5)
= (-5x3 . 2x2) + (-5x3 . 3x) - (-5x3 . 5)
= -10x5 - 15x4 + 15x3
c) \(\left(4y^3+\frac{2}{3}y^2-\frac{1}{3}\right)3y^2\)
= 12y5 + 2y4 - y2
d) \(\left(-2x^3-\frac{1}{4}y-4yz\right)8xy^2\)
= -16x4y2 - 2xy3 - 32xy3z
a) 3x(x + 2) + 4x(-2x + 3) + (2x - 3)(3x + 1)
= 3x2 + 6x - 8x2 + 12x + 6x2 + 2x - 9x - 3
= (3x2 - 8x2 + 6x2) + (6x + 12x + 2x - 9x) - 3
= x3 + 11x - 3
b) (x2 + 1)(x2 - x + 2) - (x2 - 1)(x2 + x - 2)
= x4 - x3 + 3x2 - x + 2 - x4 - x3 + 3x2 + x - 2
= (x4 - x4) + (-x3 - x3) + (3x2 + 3x2) + (-x + x) + (2 - 2)
= -2x3 + 6x2
c) (-2x - 3)2 + (3x + 2)2 + (4x + 1)
= 4x2 + 12x + 9 + 9x2 + 12x + 4 + 4x + 1
= (4x2 + 9x2) + (12x + 12x + 4x) + (9 + 4 + 1)
= 13x2 + 28x + 14
\(\left(-2x^3-\dfrac{1}{4}y-4yz\right).8xy^2\)
\(=-2x^3.8xy^2-\dfrac{1}{4}y.8xy^2-4yz.8xy^2\)
\(=-16x^4y^2-2xy^3-32xy^3z\)
Chúc bạn học tốt!!!
\(-\dfrac{1}{3}xz\left(-9xy+15yz\right)+3x^2\left(2yz^2-yz\right)\)
\(=-\dfrac{1}{3}xz\cdot-9xy+-\dfrac{1}{3}xz\cdot15yz+3x^2\cdot2yz^2-3x^2\cdot yz\)
\(=\left(-\dfrac{1}{3}\cdot-9\right)\left(x\cdot x\right)yz+\left(-\dfrac{1}{3}\cdot15\right)xy\left(z\cdot z\right)+\left(3.2\right)\left(x^2\cdot yz^2\right)-3\left(x^2\cdot yz\right)\)
=\(3x^2yz+-5xyz^2+6x^2yz^2-3x^2yz\)
\(=\left(3x^2yx-3x^2yx\right)-5x^2yz^2+6x^2yz\)
\(=-5x^2yz^2+6x^2yz\)