Question

разложите на множители: 1)81а^4-1/9b^2
2)64a^2-(a-1)^2
3) x^3 +27y^6

Answer 1

$1)81a^{4}-\frac{1}{9}b^{2}=(9a^{2})^{2}-(\frac{1}{3}b)^{2}=(9a^{2} -\frac{1}{3} b)(9a^{2}+\frac{1}{3}b)\\\\2)64a^{2} -(a-1)x^{2}=(8a)^{2}-(a-1)^{2}=(8a-a+1)(8a+a-1)=(7a+1)(9a-1)\\\\3)x^{3}+27y^{6}=x^{3}+(3y^{2})^{3}=(x+3y^{2})(x^{2}-3xy^{2}+9y^{4})$