How much greater is #-12x^2 - 19x + 8# than #-15x^2 + 17x - 18#?

Question

Nathan Axel · Accepted Answer

#(-12x^2-19x+8)-(-15x^2+17x-18)#

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

Genesis Allen · Answer

undefined To find how much greater $-12x^2 - 19x + 8$ is than $-15x^2 + 17x - 18$, subtract the second expression from the first:

$(-12x^2 - 19x + 8) - (-15x^2 + 17x - 18)$

This simplifies to:

$-12x^2 - 19x + 8 + 15x^2 - 17x + 18$

Combining like terms:

$(15x^2 - 12x^2) + (-19x - 17x) + (8 + 18)$

$(3x^2) + (-36x) + (26)$

So, $-12x^2 - 19x + 8$ is $3x^2 - 36x + 26$ greater than $-15x^2 + 17x - 18$.

Nathan Axel · Answer

undefined To find how much greater $ -12x^2 - 19x + 8 $ is than $ -15x^2 + 17x - 18 $, we need to subtract the second expression from the first:

$$ (-12x^2 - 19x + 8) - (-15x^2 + 17x - 18) $$

$$ = -12x^2 - 19x + 8 + 15x^2 - 17x + 18 $$

$$ = (-12x^2 + 15x^2) + (-19x - 17x) + (8 + 18) $$

$$ = 3x^2 - 36x + 26 $$

So, $ -12x^2 - 19x + 8 $ is $ 3x^2 - 36x + 26 $ greater than $ -15x^2 + 17x - 18 $.