factorize 1) 2x³+2xy²+2xy²
2) 5y²-20y-8z+2yz
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Question 1
Factor the given expressions using identity:
(x+y)2= x2 +y2 +2xy
(x-y)2= x2 +y2 -2xy
x2 –y2 = (x-y) (x+y)
(i) p2 + 6p + 9
(ii) 4z2 – 4z + 1
(iii) 4p4 + 9p4 + 12p2q2
(iv) (a4 - 8a2b2 + 16b4) - 81
(v) 625 – x2 – 2xy – y2
Solution(i) p2 + 6p + 9= (p+3)2
(ii) 4z2 – 4z + 1=(2z+1)2
(iii) 4p4 + 9p4 + 12p2q2=(2p2+ 3q2)2
(iv) (a4 - 8a2b2 + 16b4) - 81=(a2-4b2)2
(v) 625 – x2 – 2xy – y2= 625 -(x2+ 2xy + y2) =(25-x-y)(25+x+y)
Question 2
Divide as directed.
(i) 5(x + 1) (2x + 5) ÷ (2x + 5)
(ii) 39x(x + 5) (y - 2) ÷ 13x(y - 2)
(iii) 12pq (p + q) (q + r) (r + p) ÷ 6pq(q + r) (r + p)
(iv) 60(y - 4) (y2 + 5y + 3) ÷ 5(y - 4)
(v) x(x + 1) (x - 2) (x + 3) ÷ x(x - 2)
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