Polynomials

multiplying a polynomial by a monomial

100

3x(x² - 5x + 5)

3x³ - 15x² + 15x

200

4x²(3x² - 4x + 7)

12x⁴ - 16x³ + 28x²

300

x²(5x + 5) + 12x(4x - 6)

5x³ + 53x² - 72x

400

-2(x + 1) + x = 7 – 4x

x = 3

500

x(2x + 3) + 20 = 2x(x – 3)

x = -20/9

multiplying two polynomials

100

(x + 3)(x + 5)

x² + 8x + 15

200

(4x + 4)(8x - 5)

32x² + 12x - 20

300

(x + 4)(x² - 2x + 6)

x³ + 2x² - 2x + 24

400

(4x + 8)(4x² - 7x + 9)

16x³ + 4x² - 20x + 72

500

(x² - 12x + 5)(4x² + 3x - 6)

4x⁴ - 45x³ - 22x² + 87x - 30

square of a sum

100

(x + 4)²

x² + 8x + 16

200

(x + 7)²

x² + 14x + 49

300

(4x + 1)²

16x² + 8x + 1

400

(9x + 5)²

81x² + 90x + 25

500

(5x + 11)²

25x² + 110x + 121

square of a difference

100

(x - 2)²

x² - 4x + 4

200

(x - 8)²

x² - 16x + 64

300

(2x - 3)²

4x² - 12x + 9

400

(6x - 7)²

36x² - 84x + 49

500

(12x - 8)²

144x² - 192x + 64

product of a sum and difference

100

(x + 5)(x - 5)

x² - 25

200

(x + 8)(x - 8) 

x² - 64

300

(3x + 7)(3x - 7)

9x² - 49

400

(6x + 4)(6x - 4)

36x² - 16

500

(8x + 7)(8x - 7)

64x² - 49