Q. 14.1( 30 Votes )

# Find each of the following products:

(i) (x + 6)(x+6)

(ii) (4x + 5y)(4x + 5y)

(iii) (7a + 9b)(7a + 9b)

(iv)

(v) (x^{2} + 7)(x^{2} + 7)

(vi)

Answer :

(i) As we have (x + 6)(x+6)

(x + 6)(x + 6) = (x + 6)^{2}

By using the formula;

[(a + b)^{2} = a^{2} + b^{2} + 2ab]

We get,

(x + 6)^{2} = x^{2} + (6)^{2} + 2× (x) × (6)

= x^{2} + 36 + 12x

By arranging the expression in the form of descending powers of x we get;

= x^{2} + 12x + 36

(ii) Given;

(4x + 5y)(4x + 5y)

By using the formula;

[(a + b)^{2} = a^{2} + b^{2} + 2ab]

We get,

(4x + 5y)(4x + 5y) = (4x + 5y)^{2}

(4x + 5y)^{2} = (4x)^{2} + (5y)^{2} + 2 × (4x) ×(5y)

= 16x^{2} + 25y^{2} + 40xy

(iii) Given,

(7a + 9b)(7a + 9b)

By using the formula;

[(a + b)^{2} = a^{2} + b^{2} + 2ab]

We get,

(7a + 9b)(7a + 9b) = (7a + 9b)^{2}

(7a + 9b)^{2} = (7a)^{2} + (9b)^{2} + 2 × (7a) × (9b)

= 49a^{2} + 81b^{2} + 126ab

(iv)

By using the formula (a + b)^{2}

We get;

(v) (x^{2} + 7)(x^{2} + 7)

By using the formula (a + b)^{2}

We get;

(x^{2} + 7)(x^{2} + 7) = (x^{2} + 7)^{2}

= (x^{2})^{2} +(7)^{2} + 2 × (x^{2}) × (7)

= x^{4} + 49 + 14x^{2}

(vi)

By using the formula (a + b)^{2}

We get;

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