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\(a.\left(x^2+\frac{2}{5}y\right)\left(x^2-\frac{2}{5}y\right)\\ =x^4-\frac{4}{25}y^2\)
\(b.\left(2x+y^2\right)^3\\ =8x^3+12x^2y^2+6xy^4+y^6\)
\(c.\left(3x^2-2y\right)^3\\ =27x^6-54x^4y+36x^2y^2-8y^3\)
\(\left(x+4\right)\left(x^2-4x+16\right)\\ =x^3+64\)
\(e.\left(x^2-\frac{1}{3}\right)\left(x^4+\frac{1}{3}x^2+\frac{1}{9}\right)\\ =x^6-\frac{1}{27}\)
Trả lời:
a, \(\left(2x-5\right)^3=\left(2x\right)^3-3.\left(2x\right)^2.5+3.2x.5^2-5^3=8x^3-60x^2+150x-125\)
b, \(\left(2x+3\right)\left(4x^2-6x+9\right)=\left(2x+3\right)\left[\left(2x\right)^2-2x.3+3^2\right]=\left(2x\right)^3+3^3=8x^3+9\)
c, \(\left(\frac{1}{2}x+1\right)^3=\left(\frac{1}{2}x\right)^3+3\left(\frac{1}{2}x\right)^21+3\cdot\frac{1}{2}x.1^2+1^3=\frac{1}{8}x^3+\frac{3}{4}x^2+\frac{3}{2}x+1\)
d, \(\left(x-\frac{2}{3}y\right)\left(x^2+\frac{2}{3}xy+\frac{4}{9}y^2\right)=x^3-\left(\frac{2}{3}y\right)^3=x^3-\frac{8}{27}y^3\)
Bài 1:
a) \(\frac{4}{9}x^2-y^2=\left(\frac{2}{3}x-y\right)\left(\frac{2}{3}x+y\right)\)
b) \(x^2-5=\left(x-\sqrt{5}\right)\left(x+\sqrt{5}\right)\)
c) \(4x^2+6x+9=\left(2x+2\right)^2+5\)ko hiểu ???
d) \(\frac{1}{9}x^2-\frac{4}{3}xy+4=\left(\frac{1}{3}x\right)^2-2.\frac{1}{3}x.2+2^2=\left(\frac{1}{3}x-2\right)^2\)
Bài 2:
a) \(\left(\frac{1}{2}x-\frac{1}{3}y\right)\left(\frac{1}{2}x+\frac{1}{3}y\right)=\frac{1}{4}x^2-\frac{1}{9}y^2\)
b) \(\left(2x-\frac{1}{3}y\right)\left(4x^2+\frac{2}{3}xy+\frac{1}{9}x^2\right)=8x^3-\frac{1}{27}y^3\)
c) \(\left(3x-5y\right)\left(9x^2+15xy+\frac{1}{9}x^2\right)=27x^3-125y^3\)