Question

Помогите пожалуйста
1)(5х-4y)^2
2)121b^4-36d^6
3)(xy+z)^3
4)(3m-4)^3
5)125a^3-b^3
6)64n^3-8k^3​

Answer 1

$1) \: \: \: {(5x - 4y)}^{2} = {25x}^{2} - 40xy + {16y}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ 2) \: \: \: {121b}^{4} - {36d}^{6} = ( {11b}^{2} - {6d}^{3} )( {11b}^{2} + {6d}^{3} )$

$3) \: \: \: {(xy + z)}^{3} = {x}^{3} {y}^{3} + 3 {x}^{2} {y}^{2} z + 3xy {z}^{2} + {z}^{3}$

$4) \: \: \: {(3m - 4)}^{3} = {27m}^{3} -108 {m}^{2} + 144m - 64$

$5) \: \: \: 125 {a}^{3} - {b}^{3} = (5a - b)( {25a}^{2} + 5ab + {b}^{2} )$

$6) \: \: \: 64 {n}^{3} - 8 {k}^{3} = (4n - 2k)( {16n}^{2} + 8nk + {4k}^{2}$

Answer 2

Ответ:

1)(5х-4у)²= (5х)²-2•5х•4у+(4у)²=25х²-40ху+16у²

2) 121b⁴-36d⁶= 11²b²*²-6²b²*³=11²•(b²)²-6²•(d³)²= (11b²)²-(6b³)²= (11b²-6b³)(11b²+6b³)

3) (xy+z)³= x³y³+3x²y²z+3xyz²+z³

4)(3m-4)³= (3m)³-3•(3m)²•4+3•3m•4²-4³= 27m³-3•9m²•4+3•3m•16-64= 27m³-108m²+144m-64

5) 125a³-b³= 5³a³-b³= (5a)³-b³= (5a-b)((5a)²+5ab+b²)= (5a-b)(25a²+5ab+b²)

6) 64n³-8k³= 8(8n³-k³) = 8(2n-k)(4n²+2kn-k²)