worksheet 3.2 simplifying algebraic expressions...

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WorkSHEET 3.2 Simplifying algebraic expressions Name: ___________________ 1 For each of the following terms, find the like

terms listed in brackets. (a) 3ab (4a, 6b, −7ab, 3p, 2ab, ab) (b) −7x2 (−7x, −7, x2, −x2, 6x2) (c) 3x2y (3x2, 2x2y, 3xy2, 2x, 3y)

(d) −5a2b (−5ab2, 2a2b, 3ba2, 7

2ba , −3ab)

(a) −7ab, 2ab, ab (b) x2, −x2, 6x2 (c) 2x2y

(d) 2a2b, 3ba2, 7

2ba

2 Which of the following is an example of a constant term?

A 1 B x C x + y D −x E x2

Constant terms do not contain pronumerals (letters). The correct answer is: A

3 Simplify the following expressions by collecting like terms.

(a) qq 23 − (b) xxx 365 −+ (c) pp 2018 − (d) 12x + 8y − 7x + 3y

(a) q (b) x8 (c) 2p− (d) 12x − 7x + 8y + 3y = 5x + 11y

4 Simplify the following expressions by collecting like terms.

(a) 22 1520 yy − (b) 35711 2 +−+ xxx (c) 28 10 6 7g g g− − + + (d) 12 − 7a2b − 5 − 3ba2

(a) 25y (b) 3211 2 ++ xx (c) 28 4 7g g− − + (d) 12 − 5 − 7a2b − 3ba2 = 7 − 10a2b

5 Simplify the following expressions by collecting like terms.

(a) 222 387 pqqpqp −+ (b) xxxx 25106 22 ++− (c) 2 2 2 2 29 3 11 7a b a b ab− − + + − (d) 3m2n + 5n − 5m2n + 8n − 11

(a) 22 315 pqqp − (b) 24 7x x− + (c) 42 222 +− abba (d) 3m2n − 5m2n + 5n + 8n − 11 = −2m2n + 13n − 11

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6 Which of the following expressions cannot be simplified?

A a + 3a B 2x2 + 8x2 C 7 + 15 D m + 6 E y – y

m + 6 cannot be simplified as the expression does not contain like terms. The correct answer is: D

7 Simplify the following expressions. (a) pp 24 × (b) 3 6q pq− × (c) 10 4xy xy− ×− (d) −6ab × b × 4a

(a) 28p (b) 218pq− (c) 2240 yx (d) −24a2b2

8 Simplify the following expressions.

(a) yxx 523 ×× (b) ppqp ×−× 2311 (c) −3a2 × −4ab2 × 6a3b (d) 5de × 3d2 × −2e × 10d4e3

(a) yx 230 (b) 3 233p q− (c) 72a6b3 (d) −300d7e5

9 Simplify the following expressions.

(a) 210d

(b) 1224y

−

(c) 60 30q q− ÷− (d) −8x2y2 ÷ 15xy

(a) d5

(b) 12y

−

(c) 2

(d) 815xy

−

10 Simplify the following expressions.

(a) yxy93

(b) 4012pqrqr−

(c) 6 30abc abc÷−

(d) 3 2 4

2 2

3024x y zx yz

−

(a) 3x

(b) 103p

−

(c) 15

−

(d) 25

4xyz−

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11 Simplify:

10𝑞! × 2𝑞𝑤 × −4𝑤! × 2𝑞2𝑞 × −5𝑤! × −2𝑤 × 𝑤! × 6𝑞!

Step 1: work out if the answer is negative or positive and re-write:

= − 10𝑞! × 2𝑞𝑤 × 4𝑤! × 2𝑞

2𝑞 × 5𝑤! × 2𝑤 × 𝑤! × 6𝑞!

Step 2: do the numbers

= − 4 × 𝑞! × 𝑞𝑤 × 𝑤! × 𝑞

3 × 𝑞 × 𝑤! × 𝑤 × 𝑤! × 𝑞!

Step 3: do one letter at a time:

= − 4 𝑞! × 𝑤 × 𝑤!

3 𝑤! × 𝑤 × 𝑤! Step 4: Be careful and don’t rush it:

= − 4 𝑞!

3 𝑤

12 Simplify:

10𝑞! ÷ 2𝑞 ÷ −5𝑤!× 2𝑞𝑤 ÷ −2𝑤 × −4𝑤! ÷ 𝑤! × 2𝑞 ÷ 6𝑞!

13 Solution: Step 1: Carefully convert to a big fraction:

10𝑞! × 2𝑞𝑤 × −4𝑤! × 2𝑞2𝑞 × −5𝑤! × −2𝑤 × 𝑤! × 6𝑞!

Step 2: Now see above to Question 11 … you can see that this is No harder than the last question … J