Math scape 5.3

Question 1

Expand (x + 3)(x − 3). Hence, factorise x2 − 9.

Answer 1

x2 − 9, (x + 3)(x − 3)

Question 2

Expand (2x + 5)(2x − 5). Hence, factorise 4x2 − 25.

Answer 2

4x2 − 25, (2x + 5)(2x − 5)

Question 3

Factorise p2 − q2

Answer 3

(p − q)(p + q)

Question 4

Factorise u2 − v2

Answer 4

(u − v)(u + v)

Question 5

Factorise x2 − 4

Answer 5

(x − 2)(x + 2)

Question 6

Factorise 144 − u2

Answer 6

(12 − u)(12 + u)

Question 7

Factorise e2 − 169

Answer 7

(e − 13)(e + 13)

Question 8

Factorise 361 − j2

Answer 8

(19 − j)(19 + j)

Question 9

Factorise 4a2 − 9

Answer 9

(2a − 3)(2a + 3)

Question 10

Factorise 16e2f2 − 81g2h2

Answer 10

(4ef − 9gh)(4ef + 9gh)

Question 11

Factorise 2m2 − 18

Answer 11

2(m − 3)(m + 3)

Question 12

Factorise 80j3 − 125j

Answer 12

5j(4j − 5)(4j + 5)

Question 13

Factorise 4a2 − 36 as a difference of two squares. Has it been completely factorised?
Why?

Answer 13

(2a − 6)(2a + 6), no — each factor still has a common factor of 2.

Question 14

Factorise it completely.

Answer 14

4(a − 3)(a + 3)

Question 15

Factorise 9k2 − 36

Answer 15

9(k − 2)(k + 2)

Question 16

Factorise 4e2 − 144f2

Answer 16

4(e − 6f)(e + 6f)

Question 17

Evaluate 162 − 152 by first expressing it as (16 − 15)(16 + 15).

Answer 17

31

Question 18

Evaluate 172 − 49

Answer 18

240

Question 19

Evaluate 452 − 25

Answer 19

2000

Question 20

Factorise (a + b)2 − c2

Answer 20

(a + b − c)(a + b + c)