Question

Разложите на множители 1) 0,36x^2 − 289 2) 0,01x^8 − 0,04y^4 представьте в виде многочлена выражения 1) (9a + 9b ) ( 9a − 9b ) 2) ( 0,9m^3 + n^2 ) ( 0,9m^3 − n^2 ) 3) ( 4a^2 + 10b ) ( 4a^2 − 10b )

Answer 1

1.1)
$0.36 {x}^{2} - 289 = \\ = (0.6x)^{2} - 17^{2} = \\ = (0.6x - 17)(0.6x + 17)$
1.2)
$0.01x^{8} - 0.04 {y}^{4} = \\ = 0.01( {x}^{8} - 4y^{4} ) = \\ = 0.01( {x}^{4} - 2 {y}^{2} )( {x}^{4} + 2 {y}^{2} )$
2.1)
$(9a + 9b)(9a - 9b) = \\ = (9a)^{2} - (9b)^{2} = \\ = 81 {a}^{2} - 81 {b}^{2}$
2.2)
$(0.9 {m}^{3} + {n}^{2} )(0.9 {m}^{3} - {n}^{2}) = \\ = (0.9 {m}^{3})^{2} - ( {n}^{2} )^{2} = \\ = 0.81 {m}^{6} - {n}^{4}$
2.3)
$(4 {a}^{2} + 10b)(4 {a}^{2} - 10b) = \\ = (4 {a}^{2})^{2} - (10b)^{2} = \\ = 16 {a}^{4} - 100b^{2}$