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,

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