Question

If X = a + 3b + 4c, Y = −a + 8b − 2c and Z = −11a + 2b − 3c, ind (X + Y − Z)

Answer 1

Question :-

If X = a + 3b + 4c, Y = −a + 8b − 2c and Z = −11a + 2b − 3c, find (X + Y − Z).

Given :-

• X = a + 3b + 4c
• Y = -a + 8b - 2c
• Z = -11a + 2b - 3c

To find :-

X + Y - Z

Let us substitute the values for X,Y and Z respectively.

(a + 3b + 4c) + (-a + 8b - 2c) - (-11a + 2b - 3c)

                                              [Here (-) is being multiplied with the (+) and (-) respectively, so the signs change accordingly]

By removing the brackets,

a + 3b + 4c - a + 8b - 2c + 11a - 2b + 3c

Grouping all the like terms,

(a - a + 11a) + (3b + 8b - 2b) + (4c - 2c + 3b)

=> 11a + 9b + 5c

hence,

X + Y - Z = 11a + 9b + 5c

Important points to note :-

• (-) × (-) = (+)
• (+) × (+) = (+)
• (+) × (-) = (-)
• (-) × (+) = (-)

Hope it helps!

Happy day!