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    Can someone try and explain

    2a^2b - 8ab + 6ab^2

    so I can understand it? Thank you
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    (Original post by dottielottie)
    Can someone try and explain

    2a^2b - 8ab + 6ab^2

    so I can understand it? Thank you
    What's the full question? What do you want us to explain about it? A photo/screenshot of the question would be more preferable than ambiguous queries.
    Although, what I think you're looking for:

    Spoiler:
    Show
    Each term has a common factor, can you pull that out?
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    (Original post by dottielottie)
    Can someone try and explain

    2a^2b - 8ab + 6ab^2

    so I can understand it? Thank you
    What things do each term have in common?
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    (Original post by Zacken)
    What's the full question? What do you want us to explain about it? A photo/screenshot of the question would be more preferable than ambiguous queries.
    Although, what I think you're looking for:
    Spoiler:
    Show
    Each term has a common factor, can you pull that out?
    "Factorise the following expression" is the question
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    (Original post by dottielottie)
    "Factorise the following expression" is the question
    Did Sean's post or my spoiler help? Do you know what/how to do it now?
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    (Original post by Zacken)
    Did Sean's post or my spoiler help? Do you know what/how to do it now?
    Yes, I get that part, but the answer as a whole is not clicking for me, so I'm looking for all the steps
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    (Original post by dottielottie)
    Can someone try and explain

    2a^2b - 8ab + 6ab^2

    so I can understand it? Thank you
    1. You can multiply out a \times (b+c) to give a \times b + a \times c.

    2. We usually don't write \times in such situations, but instead write a(b+c)=ab+ac (*)

    3. Why can we turn the left hand side of equation * into the right hand side? Well, that is because you can think of, say, 3 x 5 as representing the area of a rectangle of sides 3 and 5.

    So a(b+c) says "please find the area of a rectangle of sides a and b+c" where b+c is a straight line made up of two parts of length b and c.

    Draw a picture of this rectangle and you will see that you can consider it as two smaller rectangles of area ab and ac. So equation * must be true.

    4. If I give you ab+ac, you can clearly turn this back into a(b+c). This process is called factorisation. We reverse the multiplying out process by noticing that a multiplies both b and c. It is a common factor of ab and bc and these common factors can be taken outside of a set of brackets. We call ab and bc "terms".

    5. We can factorise more complex expressions by finding all of the common factors of each term. So for example with 2a^2b - 8ab + 6ab^2, we:

    a) factorise each term completely:

    2a^2b - 8ab + 6ab^2 = 2 \times a \times a \times b + 2 \times 4 \times a \times b + 2 \times 3 \times a \times b \times b

    b) underline each factor that appears in all of the terms:

    \underline{2} \times \underline{\underline{a}} \times a \times b + \underline{2} \times 4 \times \underline{\underline{a}} \times b + \underline{2} \times 3 \times \underline{\underline{a}} \times b \times b

    I've just done 2 of the factors; you can finish off; note that you usually indicate each different factor with a different number of underline bars.

    c) take these common factors outside of a set of brackets, leaving all the rest of the factors inside:

    2a(ab+4b+3b^2)

    Note that this is not yet fully factorised; you can still find another common factor.

    d) Sometimes it's useful to factorise out a 1 as in:

    a+ab = 1 \times a + a \times b = a(1+b)

    That makes it clear that you'll leave behind a 1 in the place that a lived.
 
 
 
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