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a: \(\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)
\(=4x^2-4x+1+4-2\left(4x^2-12x+9\right)\)
\(=4x^2-4x+5-8x^2+24x-18\)
\(=-4x^2+20x-13\)
e: \(\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)=8x^3+27y^3\)
Lời giải:
a. $=(x-y)(x+y)=[(-1)-(-3)][(-1)+(-3)]=2(-4)=-8$
b. $=3x^4-2xy^3+x^3y^2+3x^2y+12xy+15y-12xy-12$
$=3x^4-2xy^3+x^3y^2+3x^2y+15y-12$
=3-2.1(-2)^3+1^3.(-2)^2+3.1^2(-2)+15(-2)-12$
$=-25$
c.
$=2x^4+3x^3y-4x^3y-12xy+12xy=2x^4-x^3y$
$=x^3(2x-y)=(-1)^3[2(-1)-2]=-1.(-4)=4$
d.
$=2x^2y+4x^2-5xy^2-10x+3xy^2-3x^2y$
$=(2x^2y-3x^2y)+4x^2+(-5xy^2+3xy^2)-10x$
$=-x^2y+4x^2-2xy^2-10x$
$=-3^2.(-2)+4.3^2-2.3(-2)^2-10.3=0$
a: Ta có: \(\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)
\(=4x^2-4x+1-2\left(4x^2-12x+9\right)+4\)
\(=4x^2-4x+5-8x^2+24x-18\)
\(=-4x^2+20x-13\)
b: \(\left(3x+2\right)^2+2\left(3x+2\right)\left(1-2y\right)+\left(1-2y\right)^2\)
\(=\left(3x+2+1-2y\right)^2\)
\(=\left(3x-2y+3\right)^2\)
a: A=2/3x^2y+4x^2y=14/3x^2y
=14/3*9*7=294
b: B=xy^2(1/2+1/3+1/6)=xy^2=3/4*1/4=3/16
c: C=x^3y^3(2+10-20)=-8x^3y^3
=-8*1^3(-1)^3=8
d: D=xy^2(2018+16-2016)
=18xy^2
=18(-2)*1/9=-4
\(F=\left(\dfrac{-1}{2}-2\right)^3-\left(\dfrac{-1}{2}+3\right)^2+\left(-2+\dfrac{3}{2}\right)^3+\left(-\dfrac{1}{2}+1\right)^2\)
\(=\dfrac{-125}{8}-\dfrac{25}{4}+\dfrac{1}{8}+\dfrac{1}{4}\)
\(=\dfrac{-124}{8}-\dfrac{24}{4}\)
=-15,5-6=-21,5
\(F=\left(-\dfrac{1}{2}-2\right)^3-\left(-\dfrac{1}{2}+3\right)^2+\left(-2+\dfrac{3}{2}\right)^3+\left(-\dfrac{1}{2}+1\right)^2\)
=-125/8+25/4-1/8+1/4
=-37/4
a) M = (x² + 3xy - 3x³) + (2y³ - xy + 3x³)
= x² + 3xy - 3x³ + 2y³ - xy + 3x³
= x² + (3xy - xy) + (-3x³ + 3x³) + 2y³
= x² + 2xy + 2y³
Tại x = 5 và y = 4
M = 5² + 2.5.4 + 2.4³
= 25 + 40 + 2.64
= 65 + 128
= 193
b) N = x²(x + y) - y(x² - y²)
= x³ + x²y - x²y + y³
= x³ + (x²y - x²y) + y³
= x³ + y³
Tại x = -6 và y = 8
N = (-6)³ + 8³
= -216 + 512
= 296
c) P = x² + 1/2 x + 1/16
= (x + 1/2)²
Tại x = 3/4 ta có:
P = (3/4 + 1/2)² = (5/4)² = 25/16
1: \(F=\left(\dfrac{-1}{2}-2\right)^3-\left(-\dfrac{1}{2}+3\right)^3+\left(-2+\dfrac{3}{2}\right)^3+\left(-\dfrac{1}{2}+1\right)^2\)
\(=\dfrac{-125}{8}-\dfrac{125}{8}+\dfrac{-1}{8}+\dfrac{1}{4}\)
\(=\dfrac{-251}{8}+\dfrac{1}{4}=\dfrac{-249}{8}\)
2:\(N=\left(-1-1\right)^2-\left(-1+\dfrac{1}{8}\right)+\left(-1+1\right)^3\)
=4+1-1/8
=5-1/8=39/8