Question

1. tính

a) \(\left(\dfrac{2}{3}x-\dfrac{3}{2}y\right)^2\)

b) \(\left(\dfrac{1}{2}x^2+\dfrac{1}{3}\right)^2\)

c) \(\left(x+\dfrac{1}{5}y^2\right)\left(x-\dfrac{1}{5}y^2\right)\)

d) \(\left(\dfrac{1}{2}x-2y\right)^3\)

e) \(\left(-\dfrac{1}{2}xy^2+x\right)^3\)

f) \(27x^3-8y^3\)

g) 4(2x - 3y) - 4 - (2x-3y)²

2. rút gọn

a) \(2m\left(5m+2\right)+\left(2m-3\right)\left(3m-1\right)\)

b) \(\left(2x+4\right)\left(8x-3\right)-\left(4x+1\right)^2\)

c) \(\left(7y-2\right)^2-\left(7y+1\right)\left(7y-1\right)\)

d) \(\left(a+2\right)^3-a\left(a-3\right)^2\)

3. c/m các biểu thức sau ko phụ thuộc vào biến x,y

a) \(\left(2x-5\right)\left(2x+5\right)-\left(2x-3\right)^2-12x\)

b) \(\left(2y-1\right)^3-2y\left(2y-3\right)^2-6y\left(2y-2\right)\)

c) \(\left(x+3\right)\left(x^2-3x+9\right)-\left(20+x^3\right)\)

d) \(3y\left(-3y-2\right)^2-\left(3y-1\right)\left(9y^2+3y+1\right)-\left(-6y-1\right)^2\)

4. Tìm x

a) \(\left(2x+5\right)\left(2x-7\right)-\left(-4x-3\right)^2=16\)

b) \(\left(8x^2+3\right)\left(8x^2-3\right)-\left(8x^2-1\right)^2=22\)

c) \(49x^2+14x+1=0\)

d) \(\left(x-1\right)^3-x\left(x-2\right)^2-\left(x-2\right)=0\)

5. c/m biểu thức luôn dương:

a) \(A=16x^2+8x+3\)

b) \(B=y^2-5y+8\)

c) C= \(2x^2-2x+2\)

d) \(D=9x^2-6x+25y^2+10y+4\)

6. Tìm GTLN và GTNN của các biểu thức sau

a) \(M=x^2+6x-1\)

b) \(N=10y-5y^2-3\)

7. thu gọn

a) \(\left(2+1\right)\left(2^2+1\right)\left(2^3+1\right)...\left(2^{32}+1\right)-2^{64}\)

b) \(\left(5+3\right)\left(5^2+3^2\right)\left(5^4+3^4\right)...\left(5^{\text{64}}+3^{64}\right)+\dfrac{5^{128}-3^{128}}{2}\)

Answer 1

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Answer 2

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