4 algebra questions please help, please?

Question

please help i dont understand this

simplify, show all factoring, if its already simplified say so.

1. a^2 - 2ab + b^2 / a + b

2. 2x^2 + x - 6 / 2x + 4

multiply and express the product in simplest form

3. 5 / 6 times 18 / 25

4. 3m / n times n^2 / 9

Answer 1

1.) (a^2 - 2ab + b^2) / (a + b), you can write this equation like this

(a^2 - ab - ab + b^2) / (a + b), [split -2ab as -ab - ab, because...read further]

Now take 'a' common from first 2 terms and '-b' common from last 2 terms (in first bracket), like this,

(a( a - b) - b(a - b) ) / (a + b)

Now take (a - b) common from the first main bracket, it will become,

(a - b) (a - b) / (a + b), simplified.

2.) write 'x'  as ' 4x - 3x' (it will remain as 'x', this method is known as middle term split method in quadratic equations)

(2x^2 + 4x - 3x - 6) / (2x + 4)

Now take common terms, it will become,

( 2x ( x + 2) - 3 (x + 2) ) / (2x + 4)

Now take (x + 2) common in the first main bracket and '2' common in the second bracket, it will become,

((x + 2) (2x - 3)) / 2(x + 2),

Now cancel the (x + 2) bracket, so the final simplified form is

(2x - 3)

Simplified.

3.) After multiplication of numerator and denominator of the first fraction (5 / 6) by numerator and denomiator of the second fraction (18 / 25), it will look like this,

(5 * 18) / (6 * 25)

Now, simplify by cancellation, (that is dividing the numerator and denominator by suitable number(s), so that further division leads to 'no-integer'.), It will become, (1 / 1) * (3 / 5) = 3 / 5 ( by dividing the numerator and denominator by 6 and 5.)

4.). It will become like this, (3m * n^2)  / (n * 9), now cancel 'n', it will become a simplified rational expression, = 3mn / 9

Answer 2

shoulda asked your parents for help over the weekend

Answer 3

1. a^2 - 2ab + b^2 / a + b

factor: a^2 - 2ab + b^2 = (a+b) (a-b)

(a+b) (a-b) / (a + b)

(a + b) are cancelled

a^2 - 2ab + b^2 / a + b = (a-b) -----> ans

2.) 2x^2 + x - 6 / 2x + 4

factor:

2x^2 + x - 6 = (2x-3) (x+2)

2x + 4 = 2( x + 2)

then;

(2x-3) (x+2) / 2 ( x + 2)

( x + 2) can now be cancelled

(2x-3) / 2 -----> ans.

3.) 5 / 6 times 18 / 25

You can reduce it to lowest term:

Now it looks like this;

1/2 times 3/5 = 3/10 ----> ans

4.) 3m / n times n^2 / 9

n^2 = n . n

3m / n times  (n . n) / 9

. : 1 n can now  be cancelled and 3 & 9 can be reduce to lowest term

Now it appears like this ;

m times n/3 = mn / 3 ----> ans.