Exercise 1

Develop the following square binomials:

1(x + 5)² =

2(2x − 5)² =

3(3x − 2)² =

4

Exercise 2

Develop the following cube binomials:

1 (2x − 3)³ =

2(x + 2)³ =

3(3x − 2)³ =

4(2x + 5)³ =

Exercise 3

Develop the following expressions:

1(3x − 2) · (3x + 2) =

2(x + 5) · (x − 5) =

3(3x − 5) · (3x − 5) =

Exercise 4

Develop the following expressions:

1(x² − x + 1)² =

2 8x³ + 27 =

38x³ − 27 =

4(x + 2) (x + 3) =

Solution of exercise 1

Develop the following square binomials:

1(x + 5)² =

= x² + 2 · x · 5 + 5² =

= x ² + 10 x + 25

2(2x − 5)² =

= (2x)² − 2 · 2x ·5 + 5² =

= 4x² − 20 x + 25

2(3x − 2)² =

= (3x)² − 2 · 3x · 2 + 2² =

= 9x² − 12x + 4

4

Solution of exercise 2

Develop the following cube binomials:

1 (2x − 3)³ = (2x)³ − 3 · (2x)² ·3 + 3 · 2x· 3² − 3³=

= 8x ³ − 36 x² + 54 x − 27

2(x + 2)³ = x³ + 3 · x² ·2 + 3 · x· 2²+ 2³ =

= x³ + 6x² + 12x + 8

3(3x − 2)³ = (3x)³ − 3 · (3x)² ·2 + 3 · 3x · 2 ² − 2³ =

= 27x ³ − 54x² + 36x − 8

4(2x + 5)³ = (2x)³ + 3 ·(2x)² · 5 + 3 · 2x · 5² + 5³ =

= 8x³ + 60 x² + 150x + 125

Solution of exercise 3

Develop the following expressions:

1(3x − 2) · (3x + 2) =

= (3x)² − 2² =

= 9x² − 4

2(x + 5) · (x − 5) =

= x² − 25

3(3x − 5) · (3x − 5) =

= (3x)² − 5² =

= 9x² − 25

Solution of exercise 4

Develop the following expressions:

1(x² − x + 1)² =

(x² − x + 1)² =

= (x²)² + (−x)² + 1² +2 · · (−x) + 2 x² · 1 + 2 · (−x) · 1=

= x4 + x² + 1 − 2x³ + 2x² − 2x=

= x4− 2x³ + 3x² − 2x + 1

2 8x³ + 27 =

(2x + 3) (4x² − 6x + 9)

38x³ − 27 =

(2x − 3) (4x² + 6x + 9)

4(x + 2) (x + 3) =

= x² + (2 + 3)x + 2 · 3 =

= x² + 5x + 6

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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.

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