(i) As we have (x + 6)(x+6)
(x + 6)(x + 6) = (x + 6)2
By using the formula;
[(a + b)2 = a2 + b2 + 2ab]
We get,
(x + 6)2 = x2 + (6)2 + 2× (x) × (6)
= x2 + 36 + 12x
By arranging the expression in the form of descending powers of x we get;
= x2 + 12x + 36
(ii) Given;
(4x + 5y)(4x + 5y)
By using the formula;
[(a + b)2 = a2 + b2 + 2ab]
We get,
(4x + 5y)(4x + 5y) = (4x + 5y)2
(4x + 5y)2 = (4x)2 + (5y)2 + 2 × (4x) ×(5y)
= 16x2 + 25y2 + 40xy
(iii) Given,
(7a + 9b)(7a + 9b)
By using the formula;
[(a + b)2 = a2 + b2 + 2ab]
We get,
(7a + 9b)(7a + 9b) = (7a + 9b)2
(7a + 9b)2 = (7a)2 + (9b)2 + 2 × (7a) × (9b)
= 49a2 + 81b2 + 126ab
(iv) \((\frac{2}{3}\text{x}\,+\frac{4}{5}y)(\frac{2}{2}\text{x}\,+\frac{4}{5}y)\)
By using the formula (a + b)2
We get;
(v) (x2 + 7)(x2 + 7)
By using the formula (a + b)2
We get;
(x2 + 7)(x2 + 7) = (x2 + 7)2
= (x2)2 +(7)2 + 2 × (x2) × (7)
= x4 + 49 + 14x2
(vi) \((\frac{5}{2}a^2+2)(\frac{5}{2}a^2+2)\)
By using the formula (a + b)2
We get;