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1)
a) 4y2-4xy+x2= x2-4xy+4y2= (x-2y)2
b) 9x2-12xy+4y2= (3x)2-2.3x.2y+(2y)2= (3x-2y)2
c) 16x2-25=(4x)2-52= (4x-5)(4x+5)
d) 1-9y2= 12-(3y)2=(1-3y)(1+3y)
g) x3-27y3= (x-3y)(x2+3xy+9y2)
h) 64 + 8x3=(4+2x)(16+8x+4x2)
a) \(\left(4x^{^5}-8x^3\right):\left(-2x^3\right)\)
\(=\left(2x^{10}-2x^9\right):\left(-2x^3\right)\)
\(=\left[2x^{10}:\left(-2x^3\right)\right]-\left[2x^9:\left(-2x^3\right)\right]\)
\(=-x^7+x^6\)
Bài 2:
\(a,=-2x^2+4\\ b,=-3x^2+4x-1\\ c,=-\dfrac{1}{2}-2xy+\dfrac{3}{2}x^2y^2\\ d,=6-8xy+2x^2y^2\\ e,=2\left(x-y\right)^2-7\left(x-y\right)+1\\ f,=\dfrac{3}{5}\left(x-y\right)^3-\dfrac{2}{5}\left(x-y\right)^2+\dfrac{3}{5}\)
Bài 2:
Ta có: \(3n^3+10n^2-5⋮3n+1\)
\(\Leftrightarrow3n^3+n^2+9n^2+3n-3n-1-4⋮3n+1\)
\(\Leftrightarrow3n+1\in\left\{1;-1;2;-2;4;-4\right\}\)
\(\Leftrightarrow3n\in\left\{0;-3;3\right\}\)
hay \(n\in\left\{0;-1;1\right\}\)
4A:
a: \(A=3xy-2x+4x^2y^2\)
\(=3\cdot\left(-1\right)\cdot2-2\cdot\left(-1\right)+4\cdot\left(-1\right)^2\cdot2^2\)
\(=-6+2+16\)
=12
Bài 1:
a: \(=15x^2-6x+5x-2\)
\(=\left(5x-2\right)\left(3x+1\right)\)
b: \(=4x^2-8x-x+2\)
\(=\left(x-2\right)\left(4x-1\right)\)
Δ ABC ∼ Δ A'B'C' theo tỉ số đồng dạng \(\dfrac{1}{2}\) nên ta có:
\(\dfrac{AB}{A'B'}\)=\(\dfrac{BC}{B'C'}\)=\(\dfrac{AC}{A'C'}\)=\(\dfrac{1}{2}\)
=>\(\dfrac{AB}{A'B'}\)=\(\dfrac{BC}{B'C'}\)=\(\dfrac{AC}{A'C'}\) =\(\dfrac{AB+BC+AC}{A'B'+B'C'+A'C'}\)= \(\dfrac{1}{2}\)
Vậy Δ ABC ∼ Δ A'B'C' theo tỉ số đồng dạng là \(\dfrac{1}{2}\)
Bài 5:
e: \(\dfrac{2}{x+1}=\dfrac{2x^2-2x+2}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(\dfrac{3}{x^2-x+1}=\dfrac{3x+3}{\left(x+1\right)\left(x^2-x+1\right)}\)