Question

★ 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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Answer 1

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 :-

1. a+b+c
2. a+b-c
3. a-b-c
4. 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.]

__________

☆ 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 :-

1. 15x² - 7x + 6
2. - x² + 5x - 10
3. - 11x² + 19x + 8
4. 3x² + 7x + 22

____________________

Answer 2

✰ Algebraic expression ✰

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❍  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,

1. a + b + c = 15x² - 7x + 4.
2. a + b - c = x² + 5x - 10.
3. a - b - c = - 11x² + 19x + 8.
4. a - b + c = 3x² + 7x + 22.

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I hope that it helps you ♡

Tʜᴀɴᴋs !!

Happy Learning !!