Expand and simplify the expression
2x(x-6)-(2x+5)(7-x)
Answers
Answer:
Simplify the following algebraic expressions.
- 6x + 5 + 12x -6
2(x - 9) + 6(-x + 2) + 4x
3x2 + 12 + 9x - 20 + 6x2 - x
(x + 2)(x + 4) + (x + 5)(-x - 1)
1.2(x - 9) - 2.3(x + 4)
(x2y)(xy2)
(-x2y2)(xy2)
Solution
Group like terms and simplify.
- 6x + 5 + 12x -6 = (- 6x + 12x) + (5 - 6)
= 6x - 1
Expand brackets.
2(x - 9) + 6(-x + 2) + 4x = 2x - 18 - 6x + 12 + 4x
Group like terms and simplify.
= (2x - 6x + 4x) + (- 18 + 12) = - 6
Group like terms and simplify.
3x2 + 12 + 9x - 20 + 6x2 - x
= (3x2 + 6x2) + (9x - x) + (12 - 20)
= 9x2 + 8x - 8
Expand brackets.
(x + 2)(x + 4) + (x + 5)(- x - 1)
= x2 + 4x + 2x + 8 - x2 - x - 5x - 5
Group like terms.
= (x2 - x2) + (4x + 2x - x - 5x) + (8 - 5)
= 3
Expand and group.
1.2(x - 9) - 2.3(x + 4)
= 1.2x - 10.8 - 2.3x - 9.2
= -1.1x - 20
Rewrite as follows.
(x2y)(xy2) = (x2 x)(y y2)
Use rules of exponential.
= x3 y3
Rewrite expression as follows.
(-x2y2)(xy2) = -(x2 x)( y2 y2)
Use rules of exponential.
= - x3 y4
Simplify the expressions.
(a b2)(a3 b) / (a2 b3)
(21 x5) / (3 x4)
(6 x4)(4 y2) / [ (3 x2)(16 y) ]
(4x - 12) / 4
(-5x - 10) / (x + 2)
(x2 - 4x - 12) / (x2 - 2 x - 24)
Solution
Use rules of exponential to simplify the numerator first.
(a b2)(a3 b) / (a2 b3) = (a4 b3) / (a2 b3)
Rewrite as follows.
(a4 / a2) (b3 / b3)
Use rule of quotient of exponentials to simplify.
= a2
Rewrite as follows.
(21 x5) / (3 x4) = (21 / 3)(x5 / x4)
Simplify.
= 7 x
(6 x4)(4 y2) / [ (3 x2)(16 y) ]
Multiply terms in numerator and denominator and simplify.
(6 x4)(4 y2) / [ (3 x2)(16 y) ] = (24 x4 y2) / (48 x2 y)
Rewrite as follows.
= (24 / 48)(x4 / x2)(y2 / y)
Simplify.
= (1 / 2) x2 y
Factor 4 out in the numerator.
(4x - 12) / 4 = 4(x - 3) / 4
Simplify.
= x - 3
Factor -5 out in the numerator.
(-5x - 10) / (x + 2) = - 5 (x + 2) / (x + 2)
Simplify.
= - 5
Factor numerator and denominator as follows.
(x2 - 4x - 12) / (x2 - 2x - 24) = [(x - 6)(x + 2)] / [(x - 6)(x + 4)]
Simplify.
= (x + 2) / (x + 4) , for all x not equal to 6
Solve for x the following linear equations.
2x = 6
6x - 8 = 4x + 4
4(x - 2) = 2(x + 3) + 7
0.1 x - 1.6 = 0.2 x + 2.3
- x / 5 = 2
(x - 4) / (- 6) = 3
(-3x + 1) / (x - 2) = -3
x / 5 + (x - 1) / 3 = 1/5
Solution
Divide both sides of the equation by 2 and simplify.
2x / 2 = 6 / 2
x = 3
Add 8 to both sides and group like terms.
6x - 8 + 8 = 4x + 4 + 8
6x = 4x + 12
Add - 4x to both sides and group like terms.
6x - 4x = 4x + 12 - 4x
2x = 12
Divide both sides by 2 and simplify.
x = 6
Expand brackets.
4x - 8 = 2x + 6 + 7
Add 8 to both sides and group like terms.
4x - 8 + 8 = 2x + 6 + 7 + 8
4x = 2x + 21
Add - 2x to both sides and group like terms.
4x - 2x = 2x + 21 - 2x
2x = 21
Divide both sides by 2.
x = 21 / 2
Add 1.6 to both sides and simplify.
0.1 x - 1.6 = 0.2 x + 2.3
0.1 x - 1.6 + 1.6 = 0.2 x + 2.3 + 1.6
0.1 x = 0.2 x + 3.9
Add - 0.2 x to both sides and simplify.
0.1 x - 0.2 x = 0.2 x + 3.9 - 0.2 x
- 0.1 x = 3.9
Divide both sides by - 0.1 and simplify.
x = - 39
Multiply both sides by - 5 and simplify.
- 5(- x / 5) = - 5(2)
x = - 10
Multiply both sides by - 6 and simplify.
(-6)(x - 4) / (- 6) = (-6)3
x - 4 = - 18
Add 4 to both sides and simplify.
x = - 14
Multiply both sides by (x - 2) and simplify.
(x - 2)(-3x + 1) / (x - 2) = -3(x - 2)
Expand right term.
-3x + 1 = -3x + 6
Add 3x to both sides and simplify.
- 3x + 1 + 3x = - 3x + 6 + 3x
1 = 6
The last statement is false and the equation has no solutions.
Multiply all terms by the LCM of 5 and 3 which is 15.
15(x / 5) + 15(x - 1) / 3 = 15(1 / 5)
Simplify and expand.
3x + 15x - 15 = 3
Group like terms and solve.
18 x = 3 + 15
18 x = 18
x = 1