Question

Question 1
Add the following algebaric expressions :
(i) t – 4tz, 2t + 6tz
(ii) 7xy, 5xy, 3xy, – 2xy
(iii) 5x – 7y, 3y – 4x + 2, 2x – 3xy – 5
(iv) m² – n² – 1, n² -1 – m², 1 – m² – n²
(v) 3x + 11 + 8z, 5x – 7
(vi) a²b + ab + ab², -a²b + 2ba + 2a²b²
(vii) x – y, y – z, z – x

Answer 1

Adding the given algebraic expressions:

• (t - 4tz) + (2t + 6tz) = (t + 2t) + (- 4tz + 6tz) = 3t + 2tz
• (7xy) + (5xy) + (3xy) + (-2xy) = 15xy - 2xy = 13xy
• (5x - 7y) + (3y - 4x + 2) + (2x - 3xy - 5)=(5x - 4x + 2x) + (-7y + 3y) - 3xy + 2 -5

                                                                     = 3x - 4y - 3xy - 3

• $m^{2}-n^{2}-1+n^{2}-1-m^{2}+1-m^{2}-n^{2}=-m^{2}-n^{2}-1$
• 3x + 11 + 8z + 5x - 7 = (3x + 5x) + 8z + ( 11 - 7) = 8x + 8z + 4

• $a^{2}b+ab+ab^{2}-a^{2}b+2ba+2a^{2}b^{2}=3ab+ab^{2}+2a^{2}b^{2}$
• x - y + y - z + z - x = (x - x) + ( - y + y) + ( - z + z) = 0 + 0 + 0 = 0

Answer 2

Given:-

add the following algebric expressions

1. (i) t – 4tz, 2t + 6tz
2. xy, 5xy, 3xy, – 2xy
3. (iii) 5x – 7y, 3y – 4x + 2, 2x – 3xy – 5
4. (iv) m² – n² – 1, n² -1 – m², 1 – m² – n²
5. (v) 3x + 11 + 8z, 5x – 7
6. (vi) a²b + ab + ab², -a²b + 2ba + 2a²b²
7. (vii) x – y, y – z, z – x

to find:-

sum of algebric expression

Solution:-

$1) t - 4tz \: + 2t + 6tz\\ \\ \: \: = t + 2tz$

$2)7xy \: \: 5xy \: \: 3xy \: \: - 2xy \\ \\ add \: all \: this \\ \\ 7xy + 5xy + 3xy + ( - 2xy) \\ \\ 15xy - 2xy \\ \\ 13xy \:$

$5x - 7y \\ 3y - 4x + 2\\ 2x - 3xy - 5 \\ \\ add \: all \: this \\ \\ 5x ( - 7y) + 3y ( - 4x) + 2 + 2x - 3xy - 5 \\ \\ 5x - 7y + 3y - 4x + 2 + 2x - 3xy - 5 \\ \\ 3x - 4y - 3$

2 )${m }^{2} - {n }^{2} - 1 \\ {n}^{2} - 1 - {m}^{2} \\ 1 - {m}^{2} - {n}^{2} \\ \\ add \: all \: this \\ \\ {m }^{2} - {n }^{2} - 1 + {n}^{2} - 1 - {m}^{2} + 1 - {m}^{2} - {n}^{2} \\ \\ - {m}^{2} - {n}^{2} - 1$

3)$3x + 11 + 8z \\ 5x - 7 \\ \\ add \: this \\ \\ 3x + 11 + 8z + 5x - 7 \\ \\ 8x + 8z + 4$

4)${a}^{2} b + ab + a {b}^{2} \\ - {a}^{2} b + 2ab + 2 {a}^{2} {b}^{2} \\ \\ add \: thiss \\ \\ {a}^{2} b + ab + a {b}^{2} + ( - {a}^{2} b) + 2ab + 2 {a}^{2} {b}^{2} \\ \\ 3ab + a {b}^{2} + 2 {a}^{2} {b}^{2}</strong><strong>5</strong><strong>)</strong><strong>$

$x - y \\ y - z \\ z - x \\ \\ add \: this \\ \\ x - y + y - z + z - x \\ \\ 0$