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May anyone please help. it will mean alot to me ​

May anyone please help. it will mean alot to me ​-example-1
User Stryder
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1 Answer

11 votes


\underline{\underline{ \huge{ \bf{Answer}}}}


\sf


1.\bf \quad(m + 11)(m - 11)

Using the algebraic identity :


\sf(a + b)(a - b) = {a}^(2) - {b}^(2)

Therefore,


\sf \longrightarrow \: {m}^(2) - {11}^(2)


\sf \longrightarrow \: {m}^(2) - 121

i.e Product of sum and difference.

___________________________________


\bf 2. \quad(y + 12)(y - 5)


\sf \longrightarrow \: y(y - 5) + 12(y - 5)


\sf \longrightarrow \: {y}^(2) - 5y + 12y - 60


\sf \longrightarrow \: {y}^(2) + 7y - 60

i.e, Product of two binomials.

____________________________________


\bf3. \quad \: (x + 15)(x + 15)


\sf \longrightarrow \: {(x + 15)}^(2)

Using the algebraic identity,


\sf {(a + b)}^(2) = {a}^(2) + {b}^(2) + 2ab


\sf \longrightarrow \: {x}^(2) + 225 + 30x

i.e, Square of a binomial.

____________________________________


\bf \: 4. \quad \: {(x - 7)}^(3)

Using the algebraic identity,


\sf \:{(a - b)}^(3) = {a}^(3) - {b}^(3) - 3ab(a - b)


\sf \longrightarrow \: {x}^(3) - 343 - 21 {x}^(2) + 147x

i.e, Cube of a binomial.

____________________________________


\bf \: 5. \quad \: {(6u + 7v + 8w)}^(2)

Using the algebraic identity,


\sf{(a + b + c)}^(2) = {a}^(2) + {b}^(2) + {c}^(2) + 2ab + 2bc + 2ca


\sf \longrightarrow \: 36 {u}^(2) + 49 {v}^(2) + 64 {w}^(2) + 84uv + 112vw + 96wu

i.e, Square of a trinomial.


\rule{200pt}{2pt}

User Mberacochea
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