173
Question
Expand the following:
(1) (p + q)2
(2) (b + 3)2
(3) (q + 7)2
(4) (n + 2)2
(5) (6 + x)2
(6) (10 + y)2
(1) (p + q)2
(2) (b + 3)2
(3) (q + 7)2
(4) (n + 2)2
(5) (6 + x)2
(6) (10 + y)2
Open in App
Solution
(1) (p + q)2
The given expression is of the form (a + b)2 .
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ (p + q)2 = p2 + 2pq + q2
(2) (b + 3)2
The given expression is of the form (a + b)2 .
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ (b + 3)2 = (b)2 + 2 (b) (3) + (3)2
= b2 + 6b + 9
(3) (q + 7)2
The given expression is of the form (a + b)2 .
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ (q + 7)2 = (q)2 + 2 (q) (7) + (7)2
= q2 + 14q + 49
(4) (n + 2)2
The given expression is of the form (a + b)2 .
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ (n + 2)2 = (n)2 + 2 (n) (2) + (2)2
= n2 + 4n + 4
(5) (6 + x)2
The given expression is of the form (a + b)2 .
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ (6 + x)2 = (6)2 + 2 (6) (x) + (x)2
= 36 + 12x + x2
(6) (10 + y)2
The given expression is of the form (a + b)2 .
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ (10 + y)2 = (10)2 + 2 (10) (y) + (y)2
= 100 + 20y + y2
The given expression is of the form (a + b)2 .
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ (p + q)2 = p2 + 2pq + q2
(2) (b + 3)2
The given expression is of the form (a + b)2 .
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ (b + 3)2 = (b)2 + 2 (b) (3) + (3)2
= b2 + 6b + 9
(3) (q + 7)2
The given expression is of the form (a + b)2 .
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ (q + 7)2 = (q)2 + 2 (q) (7) + (7)2
= q2 + 14q + 49
(4) (n + 2)2
The given expression is of the form (a + b)2 .
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ (n + 2)2 = (n)2 + 2 (n) (2) + (2)2
= n2 + 4n + 4
(5) (6 + x)2
The given expression is of the form (a + b)2 .
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ (6 + x)2 = (6)2 + 2 (6) (x) + (x)2
= 36 + 12x + x2
(6) (10 + y)2
The given expression is of the form (a + b)2 .
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ (10 + y)2 = (10)2 + 2 (10) (y) + (y)2
= 100 + 20y + y2
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