Q. 33.6( 17 Votes )

# Expand:

(i) (8a + 3b)^{2} (ii) (7x + 2y)^{2}

(iii) (5x + 11)^{2} (iv)

(v) (vi) (9x – 10)^{2}

(vii) (viii)

(ix)

Answer :

(i) Given,

(8a + 3b)^{2}

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

We get;

= (8a)^{2} + (3b)^{2} + 2 × 8a × 3b

= 64a^{2} + 9b^{2} + 48ab

(ii) (7x + 2y)^{2}

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

We get;

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

= 49x^{2} + 4y^{2} + 28xy

(iii) (5x + 11)^{2}

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

We get;

= (5x)^{2} + (11)^{2} + 2×(5x) × 11

= 25x^{2} + 121 + 110x

(iv)

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

We get;

(v)

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

We get;

(vi) (9x – 10)^{2}

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

We get;

(9x – 10)^{2}

= (9x)^{2} – 2 × (9x) × 10 + (10)^{2}

= 81x^{2} – 180x + 100

(vii) (x^{2}y – yz^{2})^{2}

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

We get;

= (x^{2}y – yz^{2})^{2}

= (x^{2}y)^{2} – 2 × (x^{2}y) × yz^{2} + (yz^{2})^{2}

= x^{4}y^{2} – 2x^{2}y^{2}z^{2} + y^{2}z^{4}

(viii)

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

We get;

(ix)

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

We get;

=

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