Exercise 1

Develop the following square binomials:

(x + 5)^2

(2x - 5)^2

(3x - 2)^2

(x^2 - \frac{1}{2}x)^2

The best Maths tutors available
1st lesson free!
Intasar
4.9
4.9 (23 reviews)
Intasar
£42
/h
1st lesson free!
Matthew
5
5 (17 reviews)
Matthew
£25
/h
1st lesson free!
Dr. Kritaphat
4.9
4.9 (6 reviews)
Dr. Kritaphat
£49
/h
1st lesson free!
Paolo
4.9
4.9 (11 reviews)
Paolo
£25
/h
1st lesson free!
Petar
4.9
4.9 (9 reviews)
Petar
£27
/h
1st lesson free!
Rajan
4.9
4.9 (11 reviews)
Rajan
£15
/h
1st lesson free!
Farooq
5
5 (13 reviews)
Farooq
£35
/h
1st lesson free!
Myriam
5
5 (15 reviews)
Myriam
£20
/h
1st lesson free!
Intasar
4.9
4.9 (23 reviews)
Intasar
£42
/h
1st lesson free!
Matthew
5
5 (17 reviews)
Matthew
£25
/h
1st lesson free!
Dr. Kritaphat
4.9
4.9 (6 reviews)
Dr. Kritaphat
£49
/h
1st lesson free!
Paolo
4.9
4.9 (11 reviews)
Paolo
£25
/h
1st lesson free!
Petar
4.9
4.9 (9 reviews)
Petar
£27
/h
1st lesson free!
Rajan
4.9
4.9 (11 reviews)
Rajan
£15
/h
1st lesson free!
Farooq
5
5 (13 reviews)
Farooq
£35
/h
1st lesson free!
Myriam
5
5 (15 reviews)
Myriam
£20
/h
First Lesson Free>

Exercise 2

Develop the following cube binomials:

(2x - 3)^3

(x + 2)^3

(3x - 2)^3

(2x + 5)^3

Exercise 3

Develop the following expressions:

(3x - 2) \cdot (3x + 2)

((x + 5) \cdot (x - 5)

(3x - 5) \cdot (3x - 5)

 

Exercise 4

Develop the following expressions:

(x^2 - x + 1)^2

2   8x^3 + 27

8x^3 - 27

4   (x + 2) (x + 3)

 

Solution of exercise 1

Develop the following square binomials:

(x + 5)^2

= x^2 + 10x + 25

 

(2x - 5)^2

= (2x)^2 - 2(2x) (5) + (-5)^2

= 4x^2 - 20x + 25

 

(3x - 2)^2

= (3x)^2 - 2 \cdot 3x \cdot 2 + 2^2

= 9x^2 - 12x + 4

 

(x^2 - \frac{1}{2}x)^2

= (x^2)^2 - 2 \cdot x^2 \cdot \frac{1}{2}x + (\frac{1}{2}x)^2

= x^4 - x^3 + \frac{1}{4}x^2

 

Solution of exercise 2

Develop the following cube binomials:

1 (2x - 3)^3 = (2x)^3 - 3 \cdot (2x)^2 \cdot 3 + 3 \cdot 2x \cdot 3^2 - 3^3

= 8x^3 - 36x^2 + 54x - 27

 

(x + 2)^3 = x^3 + 3 \cdot x^2 \cdot 2 + 3 \cdot x \cdot 2^2 + 2^3

= x^3 + 6x^2 + 12x + 8

 

3 (3x - 2)^3 = (3x)^3 - 3 \cdot (3x)^2 \cdot 2 + 3 \cdot 3x \cdot 2^2 - 2^3

= 27x^3 - 54x^2 + 36x - 8

 

4 (2x + 5)^3 = (2x)^3 + 3 \cdot (2x)^2 \cdot 5 + 3 \cdot 2x \cdot 5^2 + 5^3

= 8x^3 + 60x^2 + 150 x + 125

 

Solution of exercise 3

Develop the following expressions:

1 (3x - 2) \cdot (3x + 2)

= (3x)^2 - 2^2 = 9x^2 - 4

 

(x + 5) \cdot (x - 5)

= x^2 - 25

 

(3x - 5) \cdot (3x - 5)

= (3x)^2 - 5^2

= 9x^2 - 25

 

Solution of exercise 4

Develop the following expressions:

(x^2 - x + 1)^2

= (x^2)^2 + (-x)^2 +1^2 + 2 \cdot x^2 \cdot (-x) + 2x^2 \cdot 1 + 2 \cdot (-x) \cdot 1

= x^4 + x^2 + 1 - 2x^3 + 2x^2 - 2x

= x^4 - 2x^3 + 3x^2 - 2x + 1

 

2 8x^3 + 27

= (2x + 3) (4x^2 - 6x + 9)

 

3   8x^2 - 27

= (2x - 3) (4x^2 + 6x + 9)

 

(x + 2) (x + 3)

= x^2 + (2 + 3)x + 2 \cdot 3

= x^2 + 5x + 6

Need a Maths teacher?

Did you like the article?

1 Star2 Stars3 Stars4 Stars5 Stars 3.67/5 - 3 vote(s)
Loading...

Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.