Question

4. Simplify.

a) 5(2x + 3y) - 4(3x - 5y)
b) x - 2(x + 3y) - (2x + 3y) - 4(x + y)
c) 3(a + 2b - 2) - 2(2a - 5b - 1)

Answer 1

`a)\:5\left(2x+3y\right)-4\left(3x-5y\right)`

`\longmapsto10x+15y-4\left(3x-5y\right)`

`\longmapsto10x+15y-12x+20y`

`\longmapsto-2x+35y`

___________________________

`b)\: x - 2(x + 3y) - (2x + 3y) - 4(x + y)`

`\longmapsto x-2\left(x+3y\right)-2x-3y-4\left(x+y\right)`

`\longmapsto x-2x-6y-2x-3y-4\left(x+y\right)`

`\longmapsto x-2x-6y-2x-3y-4x-4y`

`\longmapsto-7x-13y`

___________________________

`c)\:3(a + 2b - 2) - 2(2a - 5b - 1)`

`\longmapsto3a+6b-6-2\left(2a-5b-1\right)`

`\longmapsto3a+6b-6-4a+10b+2`

`\longmapsto-a+16b-4`

____________________________

Answer 2

4. You remove the brackets

Remember:
-a × -b = positive ab / +ab
a × b = positive ab / +ab
-a × b = negative ab/ -ab
a × -b = negative ab / -ab
Where ab is the product of the two numbers & - or + are the signs.

a) 5(2x+3y) -4(3x-5y)
= 10x + 15y -12x + 20y
= 10x - 12x + 15y + 20y
= -2x + 35y
= 35y - 2x [I've been told that most people prefer the positive number in front rather than the negative number]

b) x- 2(x+ 3y) -(2x+3y) -4(x+y)b
= x - 2x - 6y - 2x - 3y - 4x - 4y
= x - 2x - 2x - 4x - 6y - 3y - 4y
= -7x - 13y

c) 3(a + 2b -2) -2(2a - 5b - 1)
= 3a + 6b - 6 -4a + 10b + 2
= 3a - 4a + 6b + 10b - 6 +2
= - a + 16b - 4
= 16b - a - 4