Question

даю 60 балліввв. подайте у вигляді квадрата двочлена вираз

Answer 1

Объяснение:

$\frac{36}{49} {p}^{8} - 12 {p}^{5} + 49 {p}^{2} = {p}^{2} ( \frac{36}{49} {p}^{6} - 12 {p}^{3} + 49) = {p}^{2} ( \frac{6}{7} {p}^{3} - 7 {)}^{2}$

$(3x + 10y {)}^{2} + (4x - 8y)(4x + 8y) = 9 {x}^{2} + 60xy + 100 {y}^{2} + 16 {x}^{2} - 64 {y}^{2} = 25 {x}^{2} + 60xy + 36 {y}^{2} = (5x + 6y {)}^{2}$

Answer 2

$\displaystyle\bf\\1)\\\\\frac{36}{49} p^{8} -12p^{5} +49p^{2} =\Big(\frac{6}{7} p^{4} \Big)^{2}-2\cdot\frac{6}{7}p^{4} \cdot7p+\Big(7p\Big)^{2} =\\\\\\=\Big(\frac{6}{7}p^{4} -7p\Big)^{2} \\\\\\2)\\\\\Big(3x+10y\Big)^{2} +\Big(4x-8y\Big)\Big(4x+8y\Big)=\\\\\\=\Big(3x\Big)^{2} +2\cdot 3x\cdot 10y+\Big(10y\Big)^{2} +\Big(4x\Big)^{2} -\Big(8y\Big)^{2} =\\\\\\=9x^{2} +60xy+100y^{2} +16x^{2} -64y^{2} =25x^{2} +60xy+36y^{2} =$

$\displaystyle\bf\\=\Big(5x\Big)^{2} +2\cdot 5x\cdot 6y+\Big(6y\Big)^{2} =\Big(5x+6y\Big)^{2}$