## SQUARE OF A TRINOMIAL WORKSHEET

Square of a Trinomial Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice problems on finding square of a trinomial.

Before look at the worksheet, if you would like to know the basic stuff on square of a trinomial,

## Square of a Trinomial Worksheet - Problems

Problem 1 :

Expand :

(5x + 3y + 2z)2

Problem 2 :

If a + b + c  =  15 , ab + bc + ac  =  25, then find the value of

a2 + b2 + c2

Problem 3 :

Expand :

(x + 2y - z)2

Problem 4 :

Expand :

(3x - y + 2z)2

Problem 5 :

Expand :

(x - 2y - 3z)2 ## Square of a Trinomial Worksheet - Solutions

Problem 1 :

Expand :

(5x + 3y + 2z)2

Solution :

(5x + 3y + 2z)is in the form of (a + b + c)2

Comparing (a + b + c)2 and (5x + 3y + 2z)2, we get

a  =  5x

b  =  3y

c  =  2z

Write the formula / expansion for (a + b + c)2.

(a + b + c)2  =  a2 + b+ c+ 2ab + 2bc + 2ac

Substitute 5x for a, 3y for b and 2z for c.

(5x + 3y + 2z)2  :

= (5x)+ (3y)+ (2z)+ 2(5x)(3y) + 2(3y)(2z) + 2(5x)(2z)

(5x + 3y + 2z)2  =  25x+ 9y+ 4z+ 30xy + 12yz + 20xz

So, the expansion of (5x + 3y + 2z)2 is

25x+ 9y+ 4z+ 30xy + 12yz + 20xz

Problem 2 :

If a + b + c  =  15 , ab + bc + ac  =  25, then find the value of

a2 + b2 + c2

Solution :

To get the value of (a2 + b2 + c2), we can use the formula or expansion of (a + b + c)2.

Write the formula / expansion for (a + b + c)2.

(a + b + c)2  =  a2 + b+ c+ 2ab + 2bc + 2ac

(a + b + c)2  =  a2 + b+ c+ 2(ab + bc + ac)

Substitute 15 for (a + b + c)  and 25 for (ab + bc + ac).

(15)2  =  a2 + b+ c+ 2(25)

225  =  a2 + b+ c+ 50

Subtract 50 from each side.

175  =  a2 + b+ c2

So, the value of a2 + b+ c2 is 175.

Problem 3 :

Expand :

(x + 2y - z)2

Solution :

(x + 2y - z)is in the form of (a + b - c)2

Comparing (a + b - c)2 and (x + 2y - z)2, we get

a  =  x

b  =  2y

c  =  z

Write the formula / expansion for (a + b - c)2.

(a + b - c)2  =  a2 + b+ c+ 2ab - 2bc - 2ac

Substitute x for a, 2y for b and z for c.

(x + 2y - z):

=  x+ (2y)+ z+ 2(x)(2y) - 2(2y)(z) - 2(x)(z)

(x + 2y - z)2  =  x+ 4y+ z+ 4xy - 4yz - 2xz

So, the expansion of (x + 2y - z)is

x+ 4y+ z+ 4xy - 4yz - 2xz

Problem 4 :

Expand :

(3x - y + 2z)2

Solution :

(3x - y + 2z)is in the form of (a - b + c)2

Comparing (a + b - c)2 and (3x - y + 2z)2, we get

a  =  3x

b  =  y

c  =  2z

Write the formula / expansion for (a - b + c)2.

(a - b + c)2  =  a2 + b+ c- 2ab - 2bc + 2ac

Substitute 3x for a, y for b and 2z for c.

(3x - y + 2z):

=  (3x)+ y+ (2z)- 2(3x)(y) - 2(y)(2z) + 2(3x)(2z)

(3x - y + 2z)2  =  9x+ y+ 4z- 6xy - 4yz + 12xz

So, the expansion of (3x - y + 2z)2 is

9x+ y+ 4z- 6xy - 4yz + 12xz

Problem 5 :

Expand :

(x - 2y - 3z)2

Solution :

(x - 2y - 3z)is in the form of (a - b - c)2

Comparing (a - b - c)2 and (x - 2y - 3z)2, we get

a  =  x

b  =  2y

c  =  3z

Write the formula / expansion for (a - b - c)2.

(a - b - c)2  =  a2 + b+ c- 2ab + 2bc - 2ac

Substitute x for a, 2y for b and 3z for c.

(x - 2y - 3z):

=  x+ (2y)+ (3z)- 2(x)(2y) + 2(2y)(3z) - 2(x)(3z)

(x - 2y - 3z)2  =  x+ 4y+ 9z- 4xy + 12yz - 6xz

So, the expansion of (x - 2y - 3z)2 is

x+ 4y+ 9z- 4xy + 12yz - 6xz After having gone through the stuff given above, we hope that the students would have understood the expansion for square of a trinomial.

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