Question

Using suitable identity simplify each of the following​

Answer 1

Answer:

here are your answer .

Step-by-step explanation:

(a).

${(a {x }^{2} - b {y}^{2} )}^{2}$

using the identity.

${(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab$

${(a {x }^{2} - b {y}^{2} )}^{2} = ({a {x}^{2} })^{2} + {(b {y}^{2}) }^{2} - 2(a {x}^{2}{b {y}^{2} })$

$= {a}^{2} {x}^{4} + {b}^{2} {y}^{4} - 2ab {x}^{2} {y}^{2}$

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(b.)

${(2a - 3b)}^{2} + (2a + 3b)^{2}$

using the identity

${(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy \\ {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy$

$(4 {a}^{2} + 9 {b}^{2} - 2(2a)(3b)) + (4 {a}^{2} + 9 {b}^{2} + 2(2a)(3b))$

$4 {a}^{2} + 9 {b}^{2} + 4 {a}^{2} + 9 {b}^{2}$

$8 {a}^{2} + 18 {b}^{2}$

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(c.)

${(3p + 6)}^{2} - {(2p - 8)}^{2}$

using the identity

$( {x}^{2} - {y}^{2} ) = (x - y)(x + y)$

$(3p + 6 - 2p + 8)(3p + 6 + 2p - 8)$

$(p + 14)(5p - 2)$

$(5 {p}^{2} + 70p - 2p - 28)$

$5 {p}^{2} + 68p - 28$

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(d.)

${(x - y)}^{2} + 4xy$

using the identity

${(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab$

$( {x}^{2} + {y}^{2} - 2xy + 4xy)$

${x}^{2} + {y}^{2} + 2xy$

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