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 a² + b² + c².

(b) If a + b + c = 15 and a² + b² + c² = 42, find ab + bc + ca.

(c) If a² + b² + c² = 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) x² + 9y² + 25z² + 6xy + 30yz +10 xz

(b) 4x² + y² + 16z² – 4xy + 8yz – 16zx

(c) x² + 9y² + 25z² + 6 xy – 30yz -10zx

(d) 4a² + 9b² + 16c² + 12ab – 24bc – 16ca

(e) 16a² + 49b² + 4c² – 56ab + 28bc – 16ca

(f) 49a² + 81b² + 9c² – 126ab – 54bc + 42ac

(g) 25l²+ 9m² + 16n² 30lm – 24mn – 40nl

(h) 4l² + m² + 81n² – 4lm – 18mn + 36nl

(i) 4l² + m² + 9n² + 4lm – 6mn -12nl

(j) p² + 16q² + 25 + 8pq + 40q + 10p

(k) 25x² + 4/9 y² + z² + 15xy + 3yz + 10zx

(l) 64x² + y² + 1/16 z² – 16xy – 1/2yz + 4zx

(m) 1/81 a² + 1/9 b² + 100 – 2/27ab – 20/3b + 20/9a

(n) a² + 1/9 b² + 25 + 2/3 ab + 10/3 b + 10a


2. (a) 2x² + 2y2 + 2z2 + 4yz

(b) 4xz – 4yz

(c) 18l² + 8m² + 2n² – 24 lm

(d) 12√2p + 24r

(e) -20/3 ab + 80ac


3. (a) 52

(b) 183/2

(c) ± 11

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