Question

Find the product using suitable identity : ( x^2/(3 ) + 4y ) ( x^2/3 – 4y )
Find the product of ( 3p^2 – 2pq + 2q^2 ) and ( 2p – 3q )
Evaluate (2.2)^2 using suitable identity

Answer 1

Find the product using suitable identity : ( x^2/(3 ) + 4y ) ( x^2/3 – 4y )

$( \frac{ {x}^{2} }{3} + 4y ) ( \frac{ {x}^{2} }{3} – 4y ) \\ using \: property \: {a - {b}^{2} }^{2} = (a + b)(a - b) \: hence \\ ( \frac{ {x}^{2} }{3} + 4y ) ( \frac{ {x}^{2} }{3} – 4y ) = { (\frac{ {x}^{2} }{3}) }^{2} - {(4y)}^{2} \\ = \frac{ {x}^{4} }{9} - 16 {y}^{2}$

Find the product of ( 3p^2 – 2pq + 2q^2 ) and ( 2p – 3q )

$( 3p^2 – 2pq + 2q^2 ) \times ( 2p – 3q ) \\ = 6 {p}^{3} - 3 {p}^{2} q - 4 {p}^{2} q + 6p {q}^{2} + 4p {q}^{2} - 6 {q}^{3} \\ = 6 {p}^{3} - 7 {p}^{2} q + 10p {q}^{2} - 6 {q}^{3}$

Evaluate (2.2)^2 using suitable identity

$(2.2)^2 = {(2 + 0.2)}^{2} \\ = {2}^{2} + {(0.2)}^{2} + 2 \times 2 \times 0.2 \\ = 4 + 0.04 + 0.8 \\ = 4.84$