Exercise 6.2
1. Add the following algebraic expressions:
(i) 3a2b, −4a2b, 9a2b
Solution:
To add the like terms, we proceed as follows:
3a2b + (-4a2b) + 9a2b
= 3a2b – 4a2b + 9a2b (Distributive Law)
= 8a2b
(iii) 4xy2–7x2y,12x2y–6xy2, −3x2y+5xy2
Solution:
To add, we proceed as follows:
(4xy2–7x2y)+(12x2y)+(−6xy2)+(−3x2y+5xy2)
= 4xy2–7x2y+12x2y–6xy2–3x2y+5xy2
= 4xy2–6xy2+5xy2–7x2y+12x2y–3x2y (Collecting like terms)
= 3xy2+2x2y (Combining like terms)
(iv) 32a – 54b+25c, 23a–72b+72c, 53a+52b–54c
Solution:
(v) 112xy+125y+137x, −112y–125x–137xy
Solution:
(vi) 72x3–12x2+53, 32x3+74x2–x+13 ,32x2–52x–2
Solution:
2. Subtract:
(i) -5xy from 12xy
Solution:
12xy – (–5xy)
= 12xy + 5xy = 17xy
(ii) 2a2 from -7a 2
Solution:
–7a2 – (2a2)
= –7a2 – 2a2 = –9a2
(iii) 2a – b from 3a – 5b
Solution:
(3a – 5b) – (2a – b)
= (3a – 5b) – 2a + b
= 3a – 5b – 2a + b
= 3a – 2a – 5b + b = a – 4b
(iv) 2x3 – 4x2 + 3x + 5 from4x3 + x2 + x + 6
Solution:
(4×3+x2+x+6)–(2×3–4×2+3x+5)
= 4×3+x2+x+6–2×3+4×2–3x–5
= 4×3–2×3+x2+4×2+x–3x+6–5 (Collecting like terms)
= 2×3+5×2–2x+1 (Combining like terms)
3. Take away:
4. Subtract 3x – 4y – 7z from the sum of x – 3y + 2z and –4x + 9y – 11z
Solution:
First add the expressions x – 3y + 2z and –4x + 9y – 11z we get:
(x – 3y + 2z ) + (–4x + 9y – 11z)
= x – 3y + 2z – 4x + 9y – 11z
= x – 4x – 3y + 9y + 2z – 11z (Collecting like terms)
= –3x + 6y – 9z (Combining like terms)
Now, Subtracting the expression 3x – 4y – 7z from the above sum, we get:
(–3x + 6y – 9z) – (3x – 4y – 7z)
= – 3x + 6y – 9z – 3x + 4y + 7z
= – 3x – 3x + 6y + 4y – 9z + 7z (Collecting like terms)
= – 6x + 10y – 2z (Combining like terms)
Thus, the answer is – 6x + 10y – 2z.
6. Subtract the sum 2x – x2 + 5 and –4x – 3 + 7x2 from 5.
Solution:
We have to subtract the sum of (2x – x2 + 5) and (–4x – 3 + 7x2) from 5.
5 – {(2x – x2 + 5) + (–4x – 3 + 7x2)}
= 5 – (2x – 4x – x2 + 7x2 + 5 – 3)
= 5 – 2x + 4x + x2 – 7x2 – 5 + 3
= 5 – 5 + 3 – 2x + 4x + x2 – 7x2 (Collecting like terms)
= 3 + 2x – 6x2 (Combining like terms)
Thus, the answer is 3 + 2x – 6x2.
7. Simplify each of the following:
(ii) [5-3x+2y-(2x-y)] – (3x-7y+9)
Solution:
[5 – 3x +2y – (2x – y)] – (3x -7y + 9)
= [5 – 3x + 2y – 2x + y] –(3x – 7y + 9)
= [5- 5x + 3y ] – (3x – 7y + 9)
= 5 – 5x + 3y – 3x + 7y = -4 – 8x + 10y