★ Hey mate, here is my QUESTION,
If,
a = 2x²+6x+6
b = 6x²-7x-9
c = 7x²-6x+7
Then find , a+b+c, a+b-c, a-b-c, a-b+c.
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Answers
Question :-
If,
a = 2x²+6x+6
b = 6x²-7x-9
c = 7x²-6x+7
Then find, a+b+c, a+b-c, a-b-c, a-b+c.
___________________
Solution :-
Given Information :-
- a = 2x²+6x+6
- b = 6x²-7x-9
- c = 7x²-6x+7
To Find :-
- a+b+c
- a+b-c
- a-b-c
- a-b+c
Calculation :-
☆ Solution 1 :-
Substituting the values given above in the equation.
⇒ a + b + c
⇒ ( 2x² + 6x + 6 ) + ( 6x² - 7x - 9 ) + ( 7x² - 6x + 7 )
Opening the brackets,
⇒ 2x² + 6x + 6 + 6x²- 7x - 9 + 7x² - 6x + 7
⇒ 15x² - 7x + 6 [Answer 1.]
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☆ Solution 2 :-
Substituting the values given above in the equation.
⇒ a + b - c
⇒ ( 2x² + 6x + 6 ) + ( 6x² - 7x - 9 ) - ( 7x² - 6x + 7 )
Opening the brackets,
⇒ 2x² + 6x + 6 + 6x² - 7x - 9 - 7x² + 6x - 7
⇒ - x² + 5x - 10 [Answer 2.]
__________
☆ Solution 3 :-
Substituting the values given above in the equation.
⇒ a - b - c
⇒ ( 2x² + 6x + 6 ) - ( 6x² - 7x - 9 ) - ( 7x² - 6x + 7 )
Opening the brackets,
⇒ 2x² + 6x + 6 - 6x² + 7x + 9 - 7x² + 6x - 7
⇒ - 11x² + 19x + 8 [Answer 3.]
__________
☆ Solution 4 :-
Substituting the values given above in the equation.
⇒ a - b + c
⇒ ( 2x² + 6x + 6 ) - ( 6x²- 7x- 9 ) + ( 7x² - 6x + 7 )
Opening the brackets,
⇒ 2x² + 6x + 6 - 6x² + 7x + 9 + 7x²- 6x + 7
⇒ 3x² + 7x + 22 [Answer 4.]
____________________
Final Answers :-
- 15x² - 7x + 6
- - x² + 5x - 10
- - 11x² + 19x + 8
- 3x² + 7x + 22
____________________
✰ Algebraic expression ✰
⠀⠀⠀━━━━━━━━━━━━━━━━━━⠀⠀⠀
❍ Gɪᴠᴇɴ Iɴғᴏ :
- ➠ a = 2x² + 6x + 6
- ➠ b = 6x² - 7x - 9
- ➠ c = 7x² - 6x + 7
⠀⠀⠀━━━━━━━━━━━━━━━━━━⠀⠀⠀
❍ Nᴇᴇᴅ Tᴏ Fɪɴᴅ :
✰ The values of :
- ➲ a + b + c,
- ➲ a + b - c,
- ➲ a - b - c,
- ➲ a - b + c.
⠀⠀⠀━━━━━━━━━━━━━━━━━━⠀⠀⠀
❍ Rᴇǫᴜɪʀᴇᴅ Sᴏʟᴜᴛɪᴏɴ :
1. Firstly, finding the value of a + b + c.
➣ Substituting the values :
➠ a + b + c
➠ (2x² + 6x + 6) + (6x² - 7x - 9) + (7x² - 6x + 7)
➣ Then, evaluating it :
➠ (2x² + 6x + 6) + (6x² - 7x - 9) + (7x² - 6x + 7)
➣ Combining the like terms (2x² + 6x² + 7x²):
➠ 15x²
➣ Combining the like terms (+ 6x - 7x - 6x):
➠ - 7x
➣ Combining the like terms (+ 6 - 9 + 7):
➠ 4
➠ Answer (1) :
- ➲ 15x² - 7x + 4.
⠀⠀⠀━━━━━━━━━━━━━━━━━━⠀⠀⠀
2. Secondly, finding the value of a + b - c.
➣ Substituting the values :
➠ a + b - c
➠ (2x² + 6x + 6) + (6x² - 7x - 9) - (7x² - 6x + 7)
➣ Then, we can write the equation as :
➠ (2x² + 6x + 6) + (6x² - 7x - 9) - (7x² + 6x - 7)
➣ Then, evaluating it :
➠ (2x² + 6x + 6) + (6x² - 7x - 9) - (7x² + 6x - 7)
➣ Combining the like terms (2x² + 6x² - 7x²):
➠ x²
➣ Combining the like terms (6x - 7x + 6x):
➠ 5x
➣ Combining the like terms (6 - 9 - 7)
➠ - 10
➠ Answer (2) :
- ➲ x² + 5x - 10.
⠀⠀⠀━━━━━━━━━━━━━━━━━━⠀⠀⠀
3. Thirdly, finding the value of a + b - c.
➣ Substituting the values :
➠ a - b - c
➠ (2x² + 6x + 6) - (6x² - 7x - 9) - (7x² - 6x + 7)
➣ Then, we can write the equation as :
➠ (2x² + 6x + 6) - (6x² + 7x + 9) - (7x² - 6x + 7)
➣ Then, evaluating it :
➠ (2x² + 6x + 6) - (6x² - 7x + 9) - (7x² + 6x - 7)
➣ Combining the like terms (2x² - 6x² - 7x²)
➠ - 11x²
➣ Combining the like terms (6x + 7x + 6x)
➠ 19x
➣ Combining the like terms (6 + 9 - 7)
➠ 8
➣ Answer (3) :
- ➲ - 11x² + 19x + 8.
⠀⠀⠀━━━━━━━━━━━━━━━━━━⠀⠀⠀
4. Fourthly, finding the value of a - b + c.
➣ Substituting the values :
➠ a - b + c
➠ (2x² + 6x + 6) - (6x² - 7x - 9) + (7x² - 6x + 7)
➣ Then, we can write the equation as :
➠ (2x² + 6x + 6) - (6x² + 7x + 9) + (7x² - 6x + 7)
➣ Then, evaluating it :
➠ (2x² + 6x + 6) - (6x² + 7x + 9) + (7x² - 6x + 7)
➣ Combining the like terms (2x² - 6x² + 7x²)
➠ 3x²
➣ Combining the like terms (6x + 7x - 6x)
➠ 7x
➣ Combining the like terms (6 + 9 + 7)
➠ 22
➣ Answer (4) :
- ➲ 3x² + 7x + 22.
⠀⠀⠀━━━━━━━━━━━━━━━━━━⠀⠀⠀
.°. Hence,
- a + b + c = 15x² - 7x + 4.
- a + b - c = x² + 5x - 10.
- a - b - c = - 11x² + 19x + 8.
- a - b + c = 3x² + 7x + 22.
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I hope that it helps you ♡
Tʜᴀɴᴋs !!
Happy Learning !!