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\(4x^2-20xy^2+25y^4=\left(2x\right)^2-2.2x.5y^2+\left(5y^2\right)^2=\left(2x-5y^2\right)^2\)
Áp dụng hằng đẳng thức: \(\left(A-B\right)^2=A^2-2AB+B^2\)
\(4x^2-20xy^2+25y^4\)
\(=\left(2x\right)^2-2\cdot2x\cdot5y^2+\left(5y\right)^2\)
\(=\left(2x-5y\right)^2\)
Ta có :
\(\left(3x^2+2y\right)\left(2y-3x^2\right)\)
\(=\left(2y+3x^2\right)\left(2y-3x^2\right)\)
\(=\left(2y\right)^2-\left(3x^2\right)^2\)
\(=4y^2-9x^4\)
= \(\left(\frac{1}{3a^3}+12b^2\right)^2\)
\(27a^3-b^3+9ab^2-27a^2b\)
\(=\left(3a\right)^3-3\cdot\left(3a\right)^2b+3\cdot3a\cdot b^2-b^3\)
\(=\left(3a-b\right)^3\)
Ta có ;
\(0.008-a^3b^6\)
\(=\left(0.2\right)^3-\left(ab^2\right)^3\)
\(=\left(0.2-ab^2\right)\left(0.04+0.2ab^2+a^2b^4\right)\)
\(0,008=0,2^3,a^6b^3=\left(a^2b\right)^3\)
=> \(0,2^3-\left(a^2b\right)^3=\left(0,2-a^2b\right)\left(0,04+0,2ab+a^4b^2\right)\)
\(4x^4-4x^2+1=\left(2x^2-1\right)^2\)
\(\left(x+2y\right)^2=x^2+4xy+4y^2\)
\(36-12x+x^2=\left(6-x\right)^2\)
\(\left(x+5y\right)^2=x^2+10xy+25y^2\)
\(4x^2-12x+9=\left(2x-3\right)^2\)
\(\left(x-2y\right)^2=x^2-4xy+4y^2\)
\(\frac{1}{4}x^6-0,01y^2=\left(\frac{1}{2}x^3\right)^2-\left(0,1y\right)^2\)
\(=\left(\frac{1}{2}x^3-0,1y\right).\left(\frac{1}{2}x^3+0,1y\right)\)
Vậy \(\frac{1}{4}x^6-0,01y^2\)\(=\left(\frac{1}{2}x^3-0,1y\right).\left(\frac{1}{2}x^3+0,1y\right)\)
Tham khảo nhé ~
\(\frac{1}{4}x^6-0.01y^2\)
\(=\left(\frac{1}{2}x^3\right)^2-\left(0.1y\right)^2\)
\(=\left(\frac{1}{2}x^3-0.1y\right)\left(\frac{1}{2}x^3+0.1y\right)\)
Mong lần này không sai nữa ......