a, (a-b).(a^2+ab+b^2)

=a(a²+ab+b²)-b(a²+ab+b²)

=a³+a²b+ab²-a²b-ab²-b³

=a³-b³+a²b-a²b+ab²-ab²

=a³-b³

 b, (2a- 3b).(4c+d)

=2a.(4c+d)-3b(4c+d)

=8ac+2ad-12bc-3bd

a) \(\left(\dfrac{1}{2}m+3\right)^3=\dfrac{m^3}{8}+\dfrac{9m^2}{4}+\dfrac{27m}{2}+9\)

b) \(2\left(m+\dfrac{1}{2}\right)=2m+1\)

c) \(\left(2\sqrt{x}+1\right)^2=4x+4\sqrt{x}+1\)

d) \(\left(2\sqrt{2}+\dfrac{1}{4}\right)^2=8+\sqrt{2}+\dfrac{1}{16}=\dfrac{129}{16}+\sqrt{2}\)

chi tiết câu c

c) \(\left(2\sqrt{x}+1\right)^2=\left(2\sqrt{x}\right)^2+2\cdot2\sqrt{x}\cdot1+1^2=4x+4\sqrt{x}+1\)

a) \(\left(\dfrac{1}{2}m+3\right)^3\)

\(=\left(\dfrac{1}{2}m\right)^3+3\cdot\left(\dfrac{1}{2}m\right)^2\cdot3+3\cdot\dfrac{1}{2}m\cdot3^2+3^3\)

\(=\dfrac{1}{8}m^3+\dfrac{9}{4}m^2+\dfrac{27}{2}m+27\)

c) Ta có: \(\left(2\sqrt{x}+1\right)^2\)

\(=\left(2\sqrt{x}\right)^2+2\cdot2\sqrt{x}\cdot1+1^2\)

\(=4x+4\sqrt{x}+1\)

Bài 3:

a) \(4x^2+4x+1=\left(2x+1\right)^2\)

b) \(9x^2-12x+4=\left(3x-2\right)^2\)

c) \(ab^2+\dfrac{1}{4}a^2b^4+1=\left(\dfrac{1}{2}ab^2+1\right)^2\)

Phần d bài 3 mk chưa lm dc

Bài 3: 

a: \(4x^2+4x+1=\left(2x+1\right)^2\)

b: \(9x^2-12x+4=\left(3x-2\right)^2\)

c: \(\dfrac{1}{4}a^2b^4+ab^2+1=\left(\dfrac{1}{2}ab^2+1\right)^2\)

d: 

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