Find the squares of the following binomials:

(1) x + 4
(2) 3 + m
(3) 3x + 1
(4) p + 2q
(5) x + 2y

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Solution

(1) x + 4
Square of (x + 4) = (x + 4)²
The expression (x + 4)² is of the form (a + b)² .
Thus, we can use the identity (a + b)² = a² + 2ab + b² .
∴ (x + 4)² = (x)² + 2 (x) (4) + (4)²
= x² + 8x + 16

(2) 3 + m
Square of (3 + m) = (3 + m)²
The expression (3 + m)² is of the form (a + b)² .
Thus, we can use the identity (a + b)² = a² + 2ab + b² .
∴ (3 + m)² = (3)² + 2 (3) (m) + (m)²
= 9 + 6m + m²

(3) 3x + 1
Square of (3x + 1)= (3x + 1)²
The expression (3x + 1)² is of the form (a + b)² .
Thus, we can use the identity (a + b)² = a² + 2ab + b² .
∴ (3x + 1)² = (3x)² + 2 (3x) (1) + (1)²
= 9x² + 6x + 1

(4) p + 2q
Square of p + 2q = (p + 2q)²
The expression (p + 2q)² is of the form (a + b)² .
Thus, we can use the identity (a + b)² = a² + 2ab + b² .
∴ (p + 2q)² = (p)² + 2 (p) (2q) + (2q)²
= p² + 4pq + 4q²

(5) x + 2y
Square of (x + 2y) = (x + 2y)²
The expression (x + 2y)² is of the form (a + b)² .
Thus, we can use the identity (a + b)² = a² + 2ab + b² .
∴ (x + 2y)² = (x)² + 2 (x) (2y) + (2y)²
= x² + 4xy + 4y²

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$(i x) {(\frac{3 a}{2} - \frac{5 b}{4})}^{2}$ $(x) (a^{2} b - b c^{2})^{2}$ $(x i) {(\frac{2 a}{3 b} + \frac{2 b}{3 a})}^{2}$ $(x i i) (x^{2} - a y)^{2}$

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Find the squares of the following binomials: (1) x + 4 (2) 3 + m (3) 3x + 1 (4) p + 2q (5) x + 2y

Find the squares of the following binomials:

(1) x + 4
(2) 3 + m
(3) 3x + 1
(4) p + 2q
(5) x + 2y