Question

27 - 125 a cube minus 135 + 225 square math solution

Answer 1

The math solution to the given equation is $27-125a^3-135a+225a^2=(3-5a)(3-5a)(3-5a)$

Step-by-step explanation:

Given equation is $27-125a^3-135a+225a^2=0$

To factorise the given equation :

• $27-125a^3-135a+225a^2=0$
• $3^3-5^3a^3-135a+15^2a^2=0$
• $=3^3+(-5a)^3+3(3)^2(-5a)+3(3)(-5a)^2$ ( by using the property $a^m.b^m=(ab)^m$ here a=5 , b=a and m=3 )
• $=3^3-(5a)63-3(3)^2(5a)+3(3)(5a)^2$
• $=(3+(-5a))^3$
• $=(3-5a)^3$ ( by using the formula $(a+b)^3=a^3+b^3+3a^2b+3ab^2$ here a=3 and b=-5a )
• $=(3-5a)\times (3-5a)\times (3-5a)$
• Therefore,  $27-125a^3-135a+225a^2=(3-5a)(3-5a)(3-5a)$

Therefore the math solution to the given equation is $27-125a^3-135a+225a^2=(3-5a)(3-5a)(3-5a)$