ADD SUBTRACT AND MULTIPLY LINEAR EXPRESSIONS WORKSHEET

1. Add (6a + 3) and (4a - 2).

2. Add (5y + 8 + 3z) and (4y - 5).

3. Subtract (6a - 3b) from (-8a + 9b).

4. Subtract (2x + 3y - 5z) from (5x - 4y - 5z).

5. Multiply (3x - 7) and (7x - 3).

6. Multiply (3a - 2b) and (2a + 3b).

7. Multiply (p + q + r) and (p + q - r).

8. Simplify : 2(3p + 5q) - 5(p + 4q) + 2(5p - 1).

9. Simplify : (3x + 5y + 3) - 2(x + 4y - 1) + 2(3x + 5).

10. Simplify : (3x + 5y + 3) - 2(x + 4y - 1) + 2(3x + 5).

1. Answer :

= (6a + 3) + (4a - 2)

 = 6a + 3 + 4a - 2

= 10a + 1

2. Answer :

= (5y + 8 + 3z) + (4y - 5)

 = 5y + 8 + 3z + 4y - 5

= 9y + 3z + 3

3. Answer :

= (-8a + 9b) - (6a - 3b)

 = -8a + 9b - 6a + 3b

= -14a + 12b

4. Answer :

= (5x - 4y - 5z) - (2x + 3y - 5z)

= 5x - 4y - 5z - 2x - 3y + 5z

= 3x - 7y

5. Answer :

= (3x - 7)(7x - 3)

= 21x² - 9x - 49x + 21

= 21x² - 58x + 21

6. Answer :

= (3a - 2b)(2a + 3b)

= 6a² + 9ab - 4ab - 6b²

= 6a² + 9ab - 4ab - 6b²

= 6a² + 5ab - 6b²

7. Answer :

= (p + q + r)(p + q - r)

Let x = p + q.

= (x + r)(x - r)

Using Algebraic Identity a² - b² = (a + b)(a - b),

= x² - r²

Substitute x = p + q.

= (p + q)² - r²

Using Algebraic Identity (a + b)² = a² + 2ab + b².

= p² + 2pq + q² - r²

8. Answer :

= 2(3p + 5q) - 5(p + 4q) + 2(5p - 1)

= 2(3p) + 2(5q) - 5(p) - 5(4q) + 2(5p) + 2(-1)

= 6p + 10q - 5p - 20q + 10p - 2

= 11p - 10q - 2

9. Answer :

= (3x + 5y + 3) - 2(x + 4y - 1) + 2(3x + 5)

= 3x + 5y + 3 - 2(x) - 2(4y) - 2(-1) + 2(3x) + 2(5)

= 3x + 5y + 3 - 2x - 8y + 2 + 6x + 10

= x - 3y + 15

10. Answer :

= (2y + 3)(y - 4) - 5y(3y - 1)

= 2y(y) + 2y(-4) + 3(y) + 3(-4) - 5y(3y) - 5y(-1)

= 2y² - 8y + 3y - 12 - 15y² + 5y

= -13y² - 12

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