What must be added to 12 x3 – 4x2 + 3x -7 to make the sum x3 + 2x2 – 3x + 2?
Answers
Given:
Two expressions:-
- 12x³ - 4x² + 3x - 7
- x³ + 2x² - 3x + 2
What To Find:
We have to find one expression that must be added to 12x³ - 4x² + 3x - 7 to get x³ + 2x² - 3x + 2.
How To Find:
To find one expression, we have to subtract 12x³ - 4x² + 3x - 7 from x³ + 2x² - 3x + 2.
Solution:
(x³ + 2x² - 3x + 2) - (12x³ - 4x² + 3x - 7)
Remove the brackets,
⇒ x³ + 2x² - 3x + 2 - 12x³ + 4x² - 3x + 7
Rearrange the like term,
⇒ x³ - 12x³ + 2x² + 4x² - 3x - 3x + 2 + 7
Solve the 1st term,
⇒ -11x³ + 2x² + 4x² - 3x - 3x + 2 + 7
Solve the 2nd term,
⇒ -11x³ + 6x² - 3x - 3x + 2 + 7
Solve the 3rd term,
⇒ -11x³ + 6x² - 6x + 2 + 7
Solve the 4th term,
⇒ -11x³ + 6x² - 6x + 9
∴ Hence, the expression is -11x³ + 6x² - 6x + 9.
Given:
Two expressions:-
12x³ - 4x² + 3x - 7
x³ + 2x² - 3x + 2
What To Find:
We have to find one expression that must be added to 12x³ - 4x² + 3x - 7 to get x³ + 2x² - 3x + 2.
How To Find:
To find one expression, we have to subtract 12x³ - 4x² + 3x - 7 from x³ + 2x² - 3x + 2.
Solution:
(x³ + 2x² - 3x + 2) - (12x³ - 4x² + 3x - 7)
Remove the brackets,
⇒ x³ + 2x² - 3x + 2 - 12x³ + 4x² - 3x + 7
Rearrange the like term,
⇒ x³ - 12x³ + 2x² + 4x² - 3x - 3x + 2 + 7
Solve the 1st term,
⇒ -11x³ + 2x² + 4x² - 3x - 3x + 2 + 7
Solve the 2nd term,
⇒ -11x³ + 6x² - 3x - 3x + 2 + 7
Solve the 3rd term,
⇒ -11x³ + 6x² - 6x + 2 + 7
Solve the 4th term,
⇒ -11x³ + 6x² - 6x + 9