Question

Factories 54m3n + 81m4n2 b) 15x2y3z + 25x3y2z + 35x2y2z​

Answer 1

Part a)

Given the expression

`54m^3n\:+\:81m^4n^2`

Apply exponent rule:
`a^(b+c)=a^ba^c`

`54m^3n\:+\:81m^4n^2=54m^3n+81m^3mnn` ∵
`m^4n^2=m^3mnn`

Rewrite 81 as 3 · 27

Rewrite 54 as 2 · 27

`=2\cdot \:27m^3n+3\cdot \:27m^3mnn`

Factor out the common term: 27m³n

`=27m^3n\left(2+3mn\right)`

Therefore,

`54m^3n\:+\:81m^4n^2=54m^3n+81m^3mnn=27m^3n\left(2+3mn\right)`

Part B)

Given the expression

`15x^2y^3z+25x^3y^2z+35x^2y^2z`

Apply exponent rule:
`a^(b+c)=a^ba^c`

`15x^2y^3z+25x^3y^2z+35x^2y^2z=15x^2y^2yz+25x^2xy^2z+35x^2y^2z`

Rewrite as

`=3\cdot \:5y^2x^2zy+5\cdot \:5y^2x^2zx+7\cdot \:5y^2x^2z`

Factor out common term 5y²x²z

`=5y^2x^2z\left(3y+5x+7\right)`

Therefore,

`15x^2y^3z+25x^3y^2z+35x^2y^2z=5y^2x^2z\left(3y+5x+7\right)`