Algebraic Manipulations

Question 1

3m + 4m + m = ?

Answer 1

8m

Question 2

8m + 2n +7m - 7n = ?

Answer 2

15m - 5n

Question 3

3x² + 4x - 5 - 7x² - 4x + 8 = ?

Answer 3

-4x² + 3

Question 4

a(x + y) = ?

Answer 4

ax + ay

Question 5

4(3x - 7) = ?

Answer 5

12x - 28

Question 6

5(2a - 5b + 3c) = ?

Answer 6

10a - 25b + 15c

Question 7

3x⁴(7x³ - 4x - 1) = ?

Answer 7

21x⁷ - 12x⁵ - 3x⁴

Question 8

4(3x - 7) - 5(4x - 2) = ?

Answer 8

12x - 28 - 20x + 10 =

-8x - 18

Question 9

(x + 4)(x + 6) = ?

Answer 9

x² + 4x + 6x + 24 =

x² + 10x + 24

Question 10

(x + 7)(x + 4) = ?

Answer 10

x² + 7x + 4x + 28 =

x² + 11x + 28

Question 11

(x - 5)(x - 2) = ?

Answer 11

x² -5x -2x + 10 =

x² - 7x + 10

Question 12

(x + 6)(x - 3) = ?

Answer 12

x² + 6x - 3x - 18 =

x² + 3x - 18

Question 13

(x + 6)(x - 8)

Answer 13

x² + 6x - 8x - 48 =

x² - 2x -48

Question 14

(x + 5)(x - 5) = ?

Answer 14

x² + 5x - 5x - 25

x² - 25

Question 15

(x + 5)² = ?

Answer 15

x² + 5x + 5x + 25 =

x² + 10x + 25

Question 16

(x - 10)² = ?

Answer 16

x² - 10x - 10x + 100 =

x² - 20x + 100

Question 17

(2x + 5)(3x - 10) = ?

Answer 17

6x² + 15x -20x - 50 =

6x² - 5x - 50

Question 18

3(x + 4)(x + 5) = ?

Answer 18

3(x² + 5x + 4x + 20) =

3(x² + 9x + 20) =

3x² + 27x + 60

Question 19

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

Answer 19

2(16x² + 12x - 12x - 9) =

2(16x² - 9)=

32x² - 18

Question 20

(a + b)(a - b) = ?

Answer 20

a² - b²

Question 21

(a - b)(a - b) = ?

Answer 21

a² - 2ab + b²

Question 22

(a + b)(a + b) = ?

Answer 22

a² + 2ab + b²

Question 23

(a + b)² = ?

Answer 23

a² + 2ab + b²

Question 24

If (x + 1/x)² = 4, what does x² + 1/x² = ?

Answer 24

(x + 1/x)(x + 1/x) = x² + 1 + 1 + 1/x²

x² + 1/x² = 4 - 2 = 2

Question 25

4x + 6y - 8 = ?

Answer 25

2(2x + 3y - 4)

Question 26

8ax + 12ay - 40az factored is ?

Answer 26

4a(2x + 3y - 10z)

Question 27

10a⁴y⁶z³ - 15a⁷y factored is ?

Answer 27

5a⁴y(2y⁵z³ - 3a³)

Question 28

x⁴y - xy³ + xy factored is ?

Answer 28

xy(x³ - y² + 1)

Question 29

9by + 12be + 4ye factored is ?

Answer 29

9by + 12be + 4ye

It cannot be modified. It’s considered prime.

Question 30

x⁴ - y⁴ factored is ?

Answer 30

(x² + y²)(x² - y²) =

x² + y²)(x + y)(x - y

Question 31

(x² - 1) factored is ?

Answer 31

(x + 1)(x - 1)

Question 32

x - 9
—– reduced and factored is ?
9 - x

Answer 32

(x - 9) 1

• ——– = —– = -1
• 1(x - 9) -1

Question 33

What is the reciprocal of 2 - ¼?

Answer 33

8/4 - 1/4 = 7/4 (then you flip it)

4/7

Question 34

x(1 - x)
——– = ?
(x - 1)

Answer 34

-x