Question

How to factorise:

1) 9t²w - 3.

2) 4(x - 5)² + 3 (x - 5)

Answer 1

1.
`3(3t^(2) w-1)`

2.
`(4x-17)(x-5)`

Explanation:

For the first question, you simply get the common factor out of both values and in this case it is 3. So if you take 3 out of
`9t^(2) w` it is basically like dividing.

*You can't divide the alphabetic variables though* So it would be 3t^2w

Then, with -3 you again divide it by 3 so it would be -1.

Put them together and you get

3(3t^2w-1)

For the second question it has some more steps than the first one.

You first expand both of them:

4(x-5)(x-5) + 3x - 15

Then you should expand the double brackets using the foil method ( search it up if confused):

`4(x^(2) -5x-5x+25) + 3x -15`

`4(x^(2) -10x+25) + 3x -15`

Then you simply the brackets where -5x and -5x makes -10x. Now take the whole bracket and times it by 4 :

`4x^(2) -40x+100 + 3x-15`

Now you simplify again:

`4x^(2) -37x+85`

You then factorise this equation right here into a double bracket:

`4x^(2) -20x-17x+85\\`

`4x(x-5)-17(x-5)`

As you could see (x-5) is the same so it works!

then you factorise it to:

`(4x-17)(x-5)`

I hope it is right and if you see any mistakes pls feel free to ask :)

Answer 2

1)=3(3t^2w-1)

2)=(4x-17)(x-5)

Explanation:

1) =Factor out 3

2) =in order to factor an integer we need to repeatedly divide it by the ascending sequence of primes (2,3,5)

number of times each prime divides the original integer becomes it's exponent in the final result. for this equation prime number 2 to the power of 2 =4

2^2(x - 5)² + 3 (x - 5)

we need to factor GCF ( greatest common factor)

The resulting term is a product of GCF and original expression divided by GCF. in equation the GCF = x-5

(x-5)(2^2(x-5)^2/x-5 + 3(x-5)/x-5 )

Need to reduce fraction to lowest terms. Done by dividing out factors that appear both in numerator and denominator. Common factor in equation is x-5

(x-5)(2^2(x-5)^2-1+3)

need to evaluate a power by multiplying the base by itself as many times as the exponent indicates. in equation base 2 will be multiplied by itself twice.

(x-5)(4(x-5)+3)

Expand this term by multiplying a term and an expression. Following product A(B+C)=AB+AC

in equation the resulting expression will consist of 2 terms:

first term is a product of 4 and X

Second term is a product of 4 and -5

(x-5)((4x-4*5)+3)

Numerical factors in this term have been multiplied

(x-5)((4x-20)+3)

We need to get rid of expression parentheses. If there is a negative sign in front of it , each term within expression changes sign. Otherwise expression remains unchanged. In equation there are no negative expression s.

(x-5)(4x-20+3)

Simplify = (4x-17)(x-5) or (x-5)(4x-17)