Worksheet on the Square of a Trinomial
Practice the questions given in the worksheet
on the square of a trinomial. To find the square of the sum of three or more
terms can be determined by the formula of the identities of the square of sum
of two terms.
See the formulas to expand using the identities
for the square of a trinomial.
1.
Expand each of the following.
(a) (x + 3y + 5z)
^{2}
(b) (2x + y + 4z)
^{2}
(c) (x – 3y + 5z)
^{2}
(d) (2a + 3b – 4c)
^{2}
(e) (4a – 7b – 2c)
^{2}
(f) (7a – 9b + 3c)
^{2}
(g) (5l + 3m – 4n)
^{2}
(h) (2l + m – 9n)
^{2}
(i) (2l + m – 3n)
^{2}
(j) (p + 4q + 5)
^{2}
(k) (5x + 3/2 y + z)
^{2}
(l) (8x – y + 1/4 z)
^{2}
(m) (1/9 a – 1/3 b + 10)
^{2}
(n)(a – 1/3 b – 5)
^{2}
2. Simplify the following
(a) (x – y – z)
^{2} + (x + y + z)
^{2}
(b) (x – y + z)
^{2} – (x – y z)
^{2}
(c) (3l – 2m + n)
^{2} + (3l – 2m – 2)
^{2}
(d) (√2 + 3p + 3√2r)
^{2} – (√2 – 3p – 3√2r)
^{2}
(e) (5a  1/3 b + 4c)
^{2} – (5a + 1/3 b – 4c)
^{2}
3. (a) If a + b + c = 10 and ab + bc + ca = 24, find the value of a
^{2} + b
^{2} + c
^{2}.
(b) If a + b + c = 15 and a
^{2} + b
^{2} + c
^{2} = 42, find ab + bc + ca.
(c) If a
^{2} + b
^{2} + c
^{2} = 49 and ab + bc + ca = 36, find a + b + c.
Answers for the worksheet
on the square of a trinomial are given below to check the exact answers of the
above expansion.
Answers:
1. (a) x
^{2} + 9y
^{2} + 25z
^{2} + 6xy + 30yz +10 xz
(b) 4x
^{2} + y
^{2} + 16z
^{2} – 4xy + 8yz – 16zx
(c) x
^{2} + 9y
^{2} + 25z
^{2} + 6 xy – 30yz 10zx
(d) 4a
^{2} + 9b
^{2} + 16c
^{2} + 12ab – 24bc – 16ca
(e) 16a
^{2} + 49b
^{2} + 4c
^{2} – 56ab + 28bc – 16ca
(f) 49a
^{2} + 81b
^{2} + 9c
^{2} – 126ab – 54bc + 42ac
(g) 25l
^{2}+ 9m
^{2} + 16n
^{2} 30lm – 24mn – 40nl
(h) 4l
^{2} + m
^{2} + 81n
^{2} – 4lm – 18mn + 36nl
(i) 4l
^{2} + m
^{2} + 9n
^{2} + 4lm – 6mn 12nl
(j) p
^{2} + 16q
^{2} + 25 + 8pq + 40q + 10p
(k) 25x
^{2} + 4/9 y
^{2} + z
^{2} + 15xy + 3yz + 10zx
(l) 64x
^{2} + y
^{2} + 1/16 z
^{2} – 16xy – 1/2yz + 4zx
(m) 1/81 a
^{2} + 1/9 b
^{2} + 100 – 2/27ab – 20/3b + 20/9a
(n) a
^{2} + 1/9 b
^{2} + 25 + 2/3 ab + 10/3 b + 10a
2. (a) 2x
^{2} + 2y2 + 2z2 + 4yz
(b) 4xz – 4yz
(c) 18l
^{2} + 8m
^{2} + 2n
^{2} – 24 lm
(d) 12√2p + 24r
(e) 20/3 ab + 80ac
3. (a) 52
(b) 183/2
(c) ± 11
Math Home Work Sheets
7th Grade Math Problems
8th Grade Math Practice
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