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Bài 4:
a) (2x)2-2.2x.(3/2)+(3/2)2=(2x-3/2)2
b) 4(x2+2x+1)-12x-3=4x2-4x+1=(2x)2-2.2x.1+12=(2x-1)2
c) (5x)2-2.5x.2y+(2y)2=(5x-2y)2
Bài 5:
a) (x+3)3
b)[ \(\left[\left(\sqrt{3}x\right)+2\right]^3\)]
c) (3x+31)3
d) \(\left[x+\sqrt{2}y\right]^3\)
Ta có: \(a+b=8\)
\(\Rightarrow\left(a+b\right)^2=8^2\)
\(\Rightarrow a^2+2ab+b^2=64\)
\(\Rightarrow a^2+2.10+b^2=64\)
\(\Rightarrow a^2+20+b^2=64\)
\(\Rightarrow a^2+b^2=44\)
\(\left(a-b\right)^2=a^2-2ab+b^2\)
\(=\left(a^2+b^2\right)-2.10\)
\(=44-20\)
\(=24\)
Vậy \(\left(a-b\right)^2=24\)
\(\text{a) }\left(\dfrac{1}{2}a^2x^4+\dfrac{4}{3}\:ax^3-\dfrac{2}{3}ax^2\right):\left(-\dfrac{2}{3}\:ax^2\right)\\ =-3ax^2-2x+1\)
\(\text{b) }4\left(\dfrac{3}{4}x-1\right)+\left(12x^2-3x\right):\left(-3x\right)-\left(2x+1\right)\\ =3x-4-4x+1-2x-1\\ =-3x-4\)
kết quả cuối cùng là: a. -\(\dfrac{3}{4}ax^2-2x+1\)
b. \(\)-\(3x-4\)
a) (–2x5 + 3x2 – 4x3) : 2x2
= (–2x5) : 2x2 + 3x2 : 2x2 + (–4x3) : 2x2
= [(–2) : 2].(x5 : x2) + (3 : 2).(x2 : x2) + [(–4) : 2].(x3 : x2)
c) (3x2y2 + 6x2y3 – 12xy) : 3xy
= (3x2y2 : 3xy) + (6x2y3 : 3xy) + ( –12xy : 3xy)
= (3 : 3).(x2 : x).(y2 : y) + (6 : 3).(x2 : x).(y3 : y) + (–12 : 3).(x : x).(y : y)
= 1.x.y + 2.xy2 + (–4).1.1
= xy + 2xy2 – 4