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September 9th, 2017, 10:24 AM  #1 
Newbie Joined: Sep 2017 From: Bristol UK Posts: 1 Thanks: 0  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 / relearn maths (failed Olevel 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. Thanks Danny 
September 9th, 2017, 01:18 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,156 Thanks: 1422 
$a^2c^2 + acd + acd + d^2 = (ac(ac) + ac(d)) + (ac(d) + d(d)) = ac(ac + d) + d(ac + d) = (ac + d)^2$

September 9th, 2017, 05:27 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,379 Thanks: 542 
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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