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September 9th, 2017, 09:24 AM   #1
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Factor by grouping - can't see how to work the problem

Hi, I'm Danny; first post on this forum.

I'm a UK adult trying to learn / re-learn maths (failed O-level exam at secondary school [high school] many years ago). This is just private study from a text book; no tutor.

I'm trying to "factor algebraic expressions by grouping" but I'm stumped on a question and can't see how to get from the question in the text book to the answer given in the back.

The question (also attached as .jpg) is:

Factorise: a^2c^2+acd+acd+d^2

and the answer is (ac+d)^2

Hoping that someone can show me how to do the working for this question.

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Danny
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September 9th, 2017, 12:18 PM   #2
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$a^2c^2 + acd + acd + d^2 = (ac(ac) + ac(d)) + (ac(d) + d(d)) = ac(ac + d) + d(ac + d) = (ac + d)^2$
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September 9th, 2017, 04:27 PM   #3
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Since a and c appear only as the product, you can simplify by letting g=ac. Also gd appears twice, so the expression can be written as $\displaystyle g^2+2gd+d^2$ which is immediately recognizable as $\displaystyle (g+d)^2$.
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