Question

Let A = 3x^2 - 5x + 7, B = 24 - 8x^2 + 9, C = 7 + 5x^2
– 3x
Find : (a) A + B - C, (b) A - 2B + C, (c) A + B + 3C
​

Answer 1

Answer :

• The value of + B - C is 33 - 2x - 10x²
• The value of A - 2B + C is 16x² - 8x - 19

• The value of A + B - 3C is 10x² - 14x + 61

Explanation :

Given :

• Value of A = 3x² - 5x + 7

• Value of B = 24 - 8x² + 9

• Value of C = 7 + 5x² - 3x

To find :

• Value of A + B - C = ?

• Value of A - 2B + C = ?

• Value of A + B + 3C = ?

Solution :

• A + B - C = ?

By substituting the value of A , B and C in the above equation , we get :

==> A + B - C

==> 3x² - 5x + 7 + 24 - 8x² + 9 - (7 + 5x² - 3x)

==> 3x² - 5x + 7 + 24 - 8x² - 7 - 5x² + 3x

==> (3x² - 8x² - 5x²) + (-5x + 3x) + (7 + 24 + 9 - 7)

==> (3x² - 13x²) - 2x + 33

==> -10x² - 2x + 33

∴ A + B - C = 33 - 2x - 10x²

• A - 2B + C = ?

By substituting the value of A , B and C in the above equation , we get :

==> A - 2B + C

==> 3x² - 5x + 7 - 2(24 - 8x² + 9) + 7 + 5x² - 3x

==> 3x² - 5x + 7 - 24 + 8x² - 9 + 7 + 5x² - 3x

==> (3x² + 8x² + 5x²) + (-5x - 3x) + (7 - 24 - 9 + 7)

==> 16x² - 8x - 19

∴ A - 2B + C = 16x² - 8x - 19

• A + B + 3C = ?

By substituting the value of A , B and C in the above equation , we get :

==> A + B - 3C

==> 3x² - 5x + 7 + 24 - 8x² + 9 + 3(7 + 5x² - 3x)

==> 3x² - 5x + 7 + 24 - 8x² + 9 + 21 + 15x² - 9x

==> (3x² - 8x² + 15x²) + (-5x - 9x) + (7 + 24 + 9 + 21)

==> 10x² - 14x + 61

∴ A + B - 3C = 10x² - 14x + 61

Therefore,

• A + B - C = 33 - 2x - 10x²

• A - 2B + C = 16x² - 8x - 19

• A + B - 3C = 10x² - 14x + 61

Answer 2

$\huge\underline\bold{\mathbb{YOUR\:QUESTION}}$

Let,

$A = 3x^{2} - 5x + 7 \\B = 24 - 8x^{2} + 9 \\C = 7 + 5x^{2}- 3x$

Find :

(a) $A + B - C$

(b) $A - 2B + C$

(c) $A + B + 3C$

$\huge\underline\bold{\mathbb{GIVEN}}$

• $A = 3x^{2} - 5x + 7$

• $B = 24 - 8x^{2} + 9$

• $C = 7 + 5x^{2}- 3x$

$\huge\underline\bold{\mathbb{SOLUTION}}$

Let's find out the value of $A + B - C.$

$A + B - C$

Putting the values of $A,\:B$ and $C.$

$\implies (3x^{2} - 5x + 7)+(24 - 8x^{2} + 9)-(7 + 5x^{2}- 3x)$

Remove parentheses.

$\implies 3x^{2} - 5x + 7+24 - 8x^{2} + 9-7 - 5x^{2}+ 3x$

Combine the like terms.

$\implies (3x^{2} - 8x^{2} - 5x^{2})+(-5x +3x) + (7+24+9-7)$

$\implies -10x^{2}-2x+33$

$\implies {\boxed{33-2x-10x^{2}}}$

$\red{\therefore A + B - C=33-2x-10x^{2}}$

$\:$

Let's find out the value of $A - 2B + C.$

$A - 2B + C$

Putting the values of $A,\:B$ and $C.$

$\implies (3x^{2} - 5x + 7)-2(24 - 8x^{2} + 9)+(7 + 5x^{2}- 3x)$

Remove parentheses.

$\implies 3x^{2} - 5x + 7-48 + 16x^{2} - 18+7 + 5x^{2}- 3x$

Combine the like terms.

$\implies (3x^{2}+ 16x^{2}+5x^{2})+( - 5x-3x) + (7-48 - 18+7)$

$\implies {\boxed{24x^{2}-8x -52}}$

$\red{\therefore A - 2B + C=24x^{2}-8x -52}$

$\:$

Let's find out the value of $A + B + 3C.$

$A + B + 3C$

Putting the values of $A,\:B$ and $C.$

$\implies (3x^{2} - 5x + 7)+(24 - 8x^{2} + 9)+3(7 + 5x^{2}- 3x)$

Remove parentheses.

$\implies 3x^{2} - 5x + 7+24 - 8x^{2} + 9+21 + 15x^{2}- 9x)$

Combine the like terms.

$\implies (3x^{2}- 8x^{2}+ 15x^{2}) +(- 5x-9x) + (7+24 + 9+21)$

$\implies {\boxed{10x^{2} -14x + 61}}$

$\red{\therefore A + B + 3C=10x^{2} -14x + 61}$

$\:$

$\huge\underline\bold{\mathbb{YOUR\:ANSWER}}$

(a) $A + B - C=33-2x-10x^{2}$

(b) $A - 2B + C=24x^{2}-8x -52$

(c) $A + B + 3C=10x^{2} -14x + 61$