Algebraic Manipulations Flashcards
3m + 4m + m = ?
8m
8m + 2n +7m - 7n = ?
15m - 5n
3x² + 4x - 5 - 7x² - 4x + 8 = ?
-4x² + 3
a(x + y) = ?
ax + ay
4(3x - 7) = ?
12x - 28
5(2a - 5b + 3c) = ?
10a - 25b + 15c
3x⁴(7x³ - 4x - 1) = ?
21x⁷ - 12x⁵ - 3x⁴
4(3x - 7) - 5(4x - 2) = ?
12x - 28 - 20x + 10 =
-8x - 18
(x + 4)(x + 6) = ?
x² + 4x + 6x + 24 =
x² + 10x + 24
(x + 7)(x + 4) = ?
x² + 7x + 4x + 28 =
x² + 11x + 28
(x - 5)(x - 2) = ?
x² -5x -2x + 10 =
x² - 7x + 10
(x + 6)(x - 3) = ?
x² + 6x - 3x - 18 =
x² + 3x - 18
(x + 6)(x - 8)
x² + 6x - 8x - 48 =
x² - 2x -48
(x + 5)(x - 5) = ?
x² + 5x - 5x - 25
x² - 25
(x + 5)² = ?
x² + 5x + 5x + 25 =
x² + 10x + 25
(x - 10)² = ?
x² - 10x - 10x + 100 =
x² - 20x + 100
(2x + 5)(3x - 10) = ?
6x² + 15x -20x - 50 =
6x² - 5x - 50
3(x + 4)(x + 5) = ?
3(x² + 5x + 4x + 20) =
3(x² + 9x + 20) =
3x² + 27x + 60
2(4x + 3)(4x - 3) = ?
2(16x² + 12x - 12x - 9) =
2(16x² - 9)=
32x² - 18
(a + b)(a - b) = ?
a² - b²
(a - b)(a - b) = ?
a² - 2ab + b²
(a + b)(a + b) = ?
a² + 2ab + b²
(a + b)² = ?
a² + 2ab + b²
If (x + 1/x)² = 4, what does x² + 1/x² = ?
(x + 1/x)(x + 1/x) = x² + 1 + 1 + 1/x²
x² + 1/x² = 4 - 2 = 2
4x + 6y - 8 = ?
2(2x + 3y - 4)
8ax + 12ay - 40az factored is ?
4a(2x + 3y - 10z)
10a⁴y⁶z³ - 15a⁷y factored is ?
5a⁴y(2y⁵z³ - 3a³)
x⁴y - xy³ + xy factored is ?
xy(x³ - y² + 1)
9by + 12be + 4ye factored is ?
9by + 12be + 4ye
It cannot be modified. It’s considered prime.
x⁴ - y⁴ factored is ?
(x² + y²)(x² - y²) =
x² + y²)(x + y)(x - y
(x² - 1) factored is ?
(x + 1)(x - 1)
x - 9
—– reduced and factored is ?
9 - x
(x - 9) 1
- ——– = —– = -1
- 1(x - 9) -1
What is the reciprocal of 2 - ¼?
8/4 - 1/4 = 7/4 (then you flip it)
4/7
x(1 - x)
——– = ?
(x - 1)
-x
