[tex] \underline{\underline{ \huge{ \bf{Answer}}}}[/tex]
[tex] \sf[/tex]
[tex]1.\bf \quad(m + 11)(m - 11)[/tex]
Using the algebraic identity :
[tex] \sf(a + b)(a - b) = {a}^{2} - {b}^{2} [/tex]
Therefore,
[tex] \sf \longrightarrow \: {m}^{2} - {11}^{2} [/tex]
[tex]\sf \longrightarrow \: {m}^{2} - 121[/tex]
i.e Product of sum and difference.
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[tex] \bf 2. \quad(y + 12)(y - 5)[/tex]
[tex]\sf \longrightarrow \: y(y - 5) + 12(y - 5)[/tex]
[tex]\sf \longrightarrow \: {y}^{2} - 5y + 12y - 60[/tex]
[tex]\sf \longrightarrow \: {y}^{2} + 7y - 60[/tex]
i.e, Product of two binomials.
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[tex] \bf3. \quad \: (x + 15)(x + 15)[/tex]
[tex]\sf \longrightarrow \: {(x + 15)}^{2} [/tex]
Using the algebraic identity,
[tex] \sf {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab[/tex]
[tex]\sf \longrightarrow \: {x}^{2} + 225 + 30x[/tex]
i.e, Square of a binomial.
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[tex] \bf \: 4. \quad \: {(x - 7)}^{3} [/tex]
Using the algebraic identity,
[tex] \sf \:{(a - b)}^{3} = {a}^{3} - {b}^{3} - 3ab(a - b)[/tex]
[tex] \sf \longrightarrow \: {x}^{3} - 343 - 21 {x}^{2} + 147x[/tex]
i.e, Cube of a binomial.
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[tex] \bf \: 5. \quad \: {(6u + 7v + 8w)}^{2} [/tex]
Using the algebraic identity,
[tex] \sf{(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca[/tex]
[tex] \sf \longrightarrow \: 36 {u}^{2} + 49 {v}^{2} + 64 {w}^{2} + 84uv + 112vw + 96wu[/tex]
i.e, Square of a trinomial.
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