72224899 Unit 4 Algebraic Expressions

Colegio Nuestra Señora del Prado (Ciudad Real) Matemáticas 2 ESO

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UNIT 4 ALGEBRAIC EXPRESSIONS

1. Un estanque cuadrado está rodeado por un seto. Expresa el número de metros que mide el seto.

2. Expresa en lenguaje algebraico la siguiente información: “El salario de un vendedor de coches se

compone de una parte fija de 1100 euros mensuales y de una parte variable de 500 euros por coche

vendido”.

3. Expresa en lenguaje algebraico la siguiente información:

a) El triple de su edad menos 5 años.

b) La mitad de su altura más 3 centímetros.

c) Su peso entre 5 más 2 kilos.

4. Find the expression:

a) I start with x, double it and then subtract 3. 2x - 3

b) I start with x, add 4 and then square the result.

c) I start with x, subtract 2, double the result and then divide by 6

d) I start with x, multiply by 4 and the subtract 2.

e) I start with x, add y and then double the result.

f) I start with x, square it and the subtract x.

g) I start with x, add 5 and the square the result

h) A brick weighs x kg. How much do 7 bricks weigh?

5. Write an equation for the following statements:

a) If you multiply a number by 3 and then add 4, the answer is 13. 3x + 4 = 13

b) The addition of a number and its consecutive is 81.

c) If you multiply the number by 2 and then subtract 5, the answer is 4.

d) If you subtract 11 from the number and then treble the result, the answer is 20.

e) If you treble the number, subtract 6 and then multiply the result by 2, you get 18.

f) If you multiply the number by 5 and subtract 4, you get the same number as when you

add 3 to the number and then double the result.

g) The addition of four consecutive numbers is 90.

h) The sum of three consecutive even numbers is 178.

6. Evaluate the polynomial – 2 + 3x – 4 at the following values of x:

a) x = 0 (-4) b) x = 1 (-2) c) x = 2 (2) d) x = - 1 (-10)

7. Evaluate the polynomial 2 - – 4x + 2 at x = - 3 - 49

8. Evaluate the following algebraic expressions at the indicated values:

a) - at x = - 1 - 2

b) + at a = 1 and b = -1 2

c) - 5abc at n = 1, a = 2, b = -1 and c = 0 3

d) – x – y - at x = - 2, y = 1 and z = - 1 2


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8. Evaluate the following algebraic expressions at the indicated values:

a) 2b at b = - 1 - 2

b) 1 – 2y at y = - 2 5

c) – 4 b + 3 at b = 1 and c = - 2 - 13

d) at x = 2 and y = 5 49

9. Evaluate the following algebraic expressions at x = - 3:

a) x – 8 - 11

b) 3 – x 6

c) 4x – 0,5 -16,5

d) 11 - 2

e) 9 - 3 - 18

f) – (1 - ) 8

g) (x – 3) . (x + 5) - 12

h) (x + 3) . ( – 1) 0

10. Collect like terms to simplify each expression:

a) 4y + 3y 7y

b) 5 + 3 - 2 + 1

c) + 3x – x + 3

d) 3x – 4 – x - 1

e) 5y + 3x + 2y + 4x

f) 2x + 3 – 5x + 7 – x - 1

11. Collect like terms to simplify each expression:

a) x + x + x + x + x 5x

b) 10x – 6x

c) 3x + 2x + x

d) a + a + b

e) + 2

12. Collect like terms to simplify the following algebraic expressions:

a) 3x + 4x 7x

b) 5 - 3 + 2

c) 4z + 6z

d) 7 y - y - 4 y

e) 2x + 5x

13. Calculate the following additions of monomials and polynomials:

a) (2 ) + (3 - 5 + x – 4) 3 - 3 + x – 4

b) (3x) + (2 + 5 x – 4)

c) (- 2 + ( + 3 – 4)

d) (- 4 ) + (2 - + 3x)

e) (3 ) + (5 – 5x + 2 )


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f) (- ) – ( + 6 + 9)

g) ( – 3 + 5x) + (-

h) (- y) + (x + 5 y – xy)

i) (4xy) + (2 – 4 xy - 3 )

j) (

) – (2x ) + (

)

14. When P(x) = 2 + 2 – x – 5 and Q(x) = + 2 – 4, calculate:

a) P(x) + Q(x) b) P(x) – Q(x)

15. Calculate the following additions and subtractions of polynomials:

a) (3 – x + 4) + (2 + 6x – 3) 5 + 5x + 1

b) (7 – 3x +5) + (2x – 5)

c) ( + 5 -2x + 1) + ( – 2 )

d) (4 – 3x + 2) – (2 + 2x + 5)

e) (- + 3x – 3) – (2x – 3)

f) (2 - 2 – 3x + 2) + ( - 2 – 3x + 5)

g) ( + 2 – 5x) – (- + 2 + 8)

h) (2 – 3x + 1) – (3 -5x +

)

i) (3 + 3 – 4x + 5) + ( - 2 + x – 4)

j) (6 - 2 + 8x) - (4 – 11x + 10)

16. When P(x) = 2 + 3 - + 5, Q(x) = - 3 + + 1 and R(x) = 3 + x, calculate:

a) P(x) + Q(x) - R(x) b) P(x) + Q(x) + R(x)

c) P(x) – Q(x) – R(x) d) P(x) – Q(x) + R(x)

e) Q(x) – P(x) – R(x)

17. Given the polynomial P(x) = 4 - 5 + 2 – 3x + 7, write down a polynomial that, added with

him, obtain the following results:

a) The polynomial 4 – 5 + 2 b) The polynomial 4 + 7

c) The polynomial -5 – 3x

18. Calculate the following additions and subtractions of polynomials:

a) (14x + 5) + (10x + 5)

b) (10x + 12) + (6x + 20)

c) (19 + 12x + 12) + (7 + 10x + 13)

d) (-13 – 5x + 14) + (-14 – 20x + 8)

e) (6x + 14) – (9x + 5)

f) (6x + 19) – (14x + 5)

g) (14 + 13x + 12) – (7 + 20x + 4)

h) (-9 - 4x – 4) – (-9 – 11x + 12)


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19. Simplify:

a) 2 . (5a) 10a

b) (-4) . 3x c) 5x . (-x) d) 2x . 3x e) 2a . (-5ab)

f) 6b . (

ab) g) (

x) . 3x h) (

x) . (

) i) 2x . (-5 y)

20. Remove brackets:

a) 3 . (1 + x) 3 + 3x

f) 2a (a – b) c) (-3x) . (x + ) d) (-5) . (1 – 2a)

e) . (a – 1) f) 3x . (2x – 3y) g) 5ab . (a + 2b)

21. Remove brackets:

a) b (1 + a + b) b) (x – 4) . (x – 3) c) (4 – 4x – 7) . (x + 3)

d)(8x + 11) (5x + 119 e) (11x + 5) (-11x + 12) f) (8x + 11) (-3x + 6)

g) (4 + 12x + 10) (-9 + 8x + 2) h) (-12x – 3) (12 – 11x + 3)

22. Simplify:

a) 5 (1 + 2x) – 5 b) 3 (x + 1) – 2 (x – 1) c) a (1 + a) – (1 + )

d)a (a – b) + b (a – b) e) 5x (2x + 3) – 4x (2x + 3) f) ab (1 – a) – ab (1 – b)

23. Calculate the product of the following monomials:

a) 3 . 5 15

b) 2 . (-3 ) c) (-2 ) . (-3 ) d) (8 y) . ( )

e) (6 ) . (

xy) f) ( ) . ( ) g) (

y) (

)

24. Calculate the product of the following expressions:

a) 6 . ( - 2 + – 3) 6 - 12 + 6 - 18

b) 2x . (3 - + 5) c) (-1) (2 + 5x – 7)

d) . ( + 5 – 3x) e) (-5x) . ( – 2x + 4)

f) (-3 ) . (-2 + 3 – 1) g) (

) . (4 - 6 – 3x)

h) (

) (

+ 6x +

) i) (-5 ) (2 -

x -

)


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25. Calculate the product of the following polynomials:

a) (x – 3) (2 + x + 1) 2 - 6 + – 2x - 3

b) (x + 3) (x – 2) c) (2x + 3) (2x – 3)

d) (2 + 3x) (2 + 3x) e) (x – 1) (2 + x)

f) (x + 5) ( – 4) g) ( -2x) (4x + 3)

h) (x +

) (3x – 2) i) (

x + 1) (x – 6)


a) (6 – 3x – 5) (2 – x + 3) 12 - 6 + 12 - 7 – 4x - 15

b) (x – 2) (2 + 5x – 3) c) ( + 1) (5 – x + 2)

d) (3 + 2x) (2 – x – 3) e) ( + x) (- + – 3)

27. Given the polynomials P(x) = 5 - + 7 +2 and Q(x) = 2 + x – 3, calculate P(x) . Q(x)

28. Given the polynomials P(x) = – 1, Q(x) = 2 – x + 3 and R(x) = 3x + 4, calculate its product.


a) 2x . (2x + 3) . 4 + 6

b) 2 . (1 – 3x) . (x + 5) c) (x + 1) (x – 1) ( + 1) d) (3 – x + 2) (-x) (2x – 1)

30. Calculate the following operations (CLUE: Use BEMDAS)

a) 5( – 2) – 2(2 – 3x + 2 ) +

(6 - 3 ) 6x – 12

b) 5 – 4(3( – x) – (2 – 3x + 4)) + 16

c) (x – 2) (2x + 1) – (1 - ) (5x – 2) 5 – 8x

d) (x + y ) (x(2y +1) – y(2x + 1) -

31. Calculate:

a) (10 ) : (2x) 5

b) (8 y) : (6 ) (4 )/(3 )

c) (2x) : (2x) d) (6a) : (-3a) e) (3b) : (6b) f) (15 ) : (3x)

g) (-8x) : (4 ) h) ( ) : (a ) i) (10x) : (5 ) j) (2 : (4a )


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32. Calculate:

a) (10 ) : (2 ) 5

b) (2 ) : x c) (3 y) . (3 ) d) 15 : (3x) e) 20 : (5x)

f) x : (2 ) g) 4 : (7x) h) 2 y : (5 ) i) (

) . (2x)

j) (

) : (-

) k) (

) : (

) l) (

) : (

)

33. Calculate:

a) (2 - 4 y + 8 ) : (2 ) x – 2y + 4

b) ( - 2 z) : (2 )

x – 2z/x

c) ( y + xy – 3x ) : (xy) d) (6x – 2xy + 4xz) : (-

x)

e) ( – x + 2y) : (2x) f) (4 a - a + 3b ) : ( a)

g) (a + 12ba - 2 a ) : (2a ) h) (2x + ) : ( )

34. Calculate:

a) (8 - 2 + 3 ) : (2x) 4 - +

b) (8 - 6 + 10 ) : (2 ) c) (15 + 12 - 21 ) : (3 )

d) (- + - ) : e) (24 - 12 - 14 ) : (2 )

f) (5 – 10 + 5 ) : (5x) g) (3 - 12 + 6 ) : (3 )

h) (3 - 7 + y) : ( y) i) (7 - z + 4 ) : ( z)

j) (2 - 5 ) : (xy) k) (10 - 15 ) : (5 )

35. Expand as in the examples:

a) + 4x + 4

b) 4 + 12x + 9

c) d) e) f) g)


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a) - 10x + 25

b) 4 - 4x + 1

c) d) e) f) g)


a) (x + 2) (x – 2) – 4

b) (2x + 3) (2x – 3) 4 – 9

c) (a + 1) (a – 1) d) (x + 4) (x – 4) e) (2x – 1) (2x + 1) f) (2a + 3b) (2a – 3b)

38. Expand the brackets:

a) + 2ab +

b)

–

- 12 +16

c) (2 +

x) (2 -

x) 4 -

d) 9 + 12 y + 4

39. Calculate the following special products:

a) + 6 + 12x + 8

b) – + 6 + 7 – 6x + 1


a) (3 – x + ) + 2x . – 2 - 4 + 7x

b) 2 – – 2x – 1

c) (x + 2) – 4 + 4 – 7x + 2

d) – . 2x + 3 - 12 + 18x

e) 3x . ( – 6) 12 + 36 + 9x

f) (2x – 3 . ) . x + 3 -10 – 12x

g) (2x – 1) . (x + 1 – ) + 2 – 3x - – 2x


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a) 2 - – – (x – 4) (x + 4) -9 + 6 + 20x + 66

b) ( + 2x – 3)) . ( – (2x – 3)) - 4 + 12x - 9

c) – – 2(4(x + 1) (x – 1) – ) 4 + 4x + 51

d) ((x – 2y) + 5) . ((x – 2y) – 5) – 4xy + 4 - 25

e) (2 – x) ( – – (x – 2) . (x – 3)) 3 – 16x +20

72224899 Unit 4 Algebraic Expressions

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