Question

(ii) 4m² - 36m + 81​

Answer 1

Step-by-step explanation:

4m^2 - 36m + 81

4m^2 - 18m - 18m + 81

2m(2m-9)-9(2m-9)

= (2m-9)^2

Answer 2

Answer:

$\mathrm{Factor}\:4m^2-36m+81:\quad \left(2m-9\right)^2$

Step-by-step explanation:

$4m^2-36m+81$

$\mathrm{Rewrite\:}4\mathrm{\:as\:}2^2$

$=2^2m^2-36m+81$

$\mathrm{Rewrite\:}81\mathrm{\:as\:}9^2$

$=2^2m^2-36m+9^2$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^mb^m=\left(ab\right)^m$

$2^2m^2=\left(2m\right)^2$

$=\left(2m\right)^2-36m+9^2$

$\mathrm{Rewrite\:}36m\mathrm{\:as\:}2\cdot \:2m\cdot \:9$

$=\left(2m\right)^2-2\cdot \:2m\cdot \:9+9^2$

$\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a-b\right)^2=a^2-2ab+b^2$

$a=2m,\:b=9$

$=\left(2m-9\right)^2$