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2.Find the product:
(i) \((5 – 2x) (3 + x)\)

(ii)\( (x + 7y) (7x – y)\)

(iii) \((a^2 + b) (a + b^2)\)

(iv)\( (p^2 – q^2)(2p + q)\)


Answer :

(i)Product of the expression:\( (5 – 2x) (3 + x)\)

\(= 5(3 + x) – 2x(3 + x)\)

\(= (5 \times 3) + (5 \times x) – (2x \times 3) – (2x \times x)\)

\(= 15 + 5x – 6x – 2x^2\)

(ii)Product of the expression: \((x + 7y) (7x – y)\)

\(= x(7x – y) + 7y(7x – y)\)

\(= (x \times 7x) – (x \times y) + (7y \times 7x) – (7y \times y)\)

\(= 7x^2 – xy + 49xy – 7y^2\)

\(= 7x^2 + 48xy – 7y^2\)

(iii)Product of the expression: \((a^2 + b) (a + b^2)\)

\(= a^2 (a + b^2) + b(a + b^2)\)

\(= (a^2 \times a) + (a^2 \times b^2) + (b \times a) + (b \times b^2)\)

\(= a^3 + a^2b^2 + ab + b^3\)

(iv)Product of the expression:\( (p^2 – q^2)(2p + q)\)

\(= p^2(2p + q) – q^2(2p + q)\)

\(= (p^2 \times 2p) + (p^2 \times q) – (q^2 \times 2p) – (q^2 \times q)\)

\(= 2p^3 + p^2q – 2pq^2 – q^3\)