Question

Розпишіть за формулами скороченого множення

Answer 1

$1)\; \; \frac{2}{9}a-1\frac{2}{16}a^3c^2=\frac{2}{9}a-\frac{9}{8}a^3c^2=\frac{2}{9}a\cdot (1-\frac{81}{16}a^2c^2)=\\\\=\frac{2}{9}a\cdot (1-\frac{9}{4}ac)\cdot (1+\frac{9}{4}ac)\\\\2)\; \; 0,001a+a^4=a\cdot (0,001+a^3)=a\cdot (0,1+a)\cdot (0,01-0,1a+a^2)\\\\3)\; \; x^5-x^4y+x^2y^3-xy^4=x^4(x-y)+xy^3(x-y)=\\\\=(x-y)(x^4+xy^3)=(x-y)\cdot x\cdot (x^3+y^3)=\\\\=x\cdot (x-y)(x+y)(x^2-xy+y^2)\\\\4)\; \; 36x^2-(1-x)^2=(6x)^2-(1-x)^2=\Big (6x-(1-x)\Big )\cdot \Big (6x+(1-x)\Big )=\\\\=(7x-1)\cdot (5x+1)$