# Binomial Worksheet

### Solutions

1Develop the following square binomials:

1(x + 5)2 =

2(2x − 5)2 =

3(3x − 2)2 =

4

2Develop the following cube binomials:

1 (2x − 3)3 =

2(x + 2)3 =

3(3x − 2)3 =

4(2x + 5)3 =

3Develop the following expressions:

1(3x − 2) · (3x + 2) =

2(x + 5) · (x − 5) =

3(3x − 5) · (3x − 5) =

4Develop the following expressions:

1(x2 − x + 1)2 =

2 8x3 + 27 =

38x3 − 27 =

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

## 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

## 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

## 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

## 4

Develop the following expressions:

1(x2 − x + 1)2 =

(x2 − x + 1)2 =

= (x2)2 + (−x)2 + 12 +2 · x2 · (−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