The question "how much greater is aa than bb?" can be expressed mathematically as:
a-b=Da−b=D
where DD is the difference between aa and bb.
The problem then is to evaluate DD in the expression:
(-12x^2-19x+8)-(-15x^2+17x-18)=D(−12x2−19x+8)−(−15x2+17x−18)=D
First distribute the minus sign to every term in the parentheses.
rArr-12x^2-19x+8-(-15x^2)-(17x)-(-18)=D⇒−12x2−19x+8−(−15x2)−(17x)−(−18)=D
rArr-12x^2-19x+8+15x^2-17x+18=D⇒−12x2−19x+8+15x2−17x+18=D
Now group similar terms.
rArr(-12x^2+15x^2)+(-19x-17x)+(8+18)=D⇒(−12x2+15x2)+(−19x−17x)+(8+18)=D
rArr(-12+15)x^2+(-19-17)x+(8+18)=D⇒(−12+15)x2+(−19−17)x+(8+18)=D
rArr3x^2-36x+26=D⇒3x2−36x+26=D
This is our answer. If we were to substitute any value of xx into the two given polynomials, the difference between them would be color(red)(3x^2-36x+26)3x2−36x+26.
Let's check our answer to prove that it is correct.
Substitute x=0x=0
-12(0)^2-19(0)+8 = 8−12(0)2−19(0)+8=8
-15(0)^2+17(0)-18 = -18−15(0)2+17(0)−18=−18
The difference between them is
8-(-18)=color(blue)268−(−18)=26
and our solution gives
3(0)^2-36(0)+26 = color(blue)263(0)2−36(0)+26=26
