Math, asked by Anonymous, 4 months ago

Using suitable identity find
(p {}^{2}  + 4)(p {}^{2}  -   \frac{1}{4} )
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Answers

Answered by Anonymous
126

\underline{\underline{\sf{\maltese\:\:Question}}}

  • Using suitable identity find  \sf{\left(p^2+4\right)\left(p^2-\dfrac{1}{4}\right)}

\underline{\underline{\sf{\maltese\:\:Answer}}}

\bf{p^4+\dfrac{15p^2}{4}-1}

\underline{\underline{\sf{\maltese\:\:Calculations}}}

Apply FOIL method :

  • (a + b)(c + d) = ac + ad + bc + bd

We Have :

\sf{\bullet\:\:\: a=p^2}

\sf{\bullet\:\:\: b=4}

\sf{\bullet\:\:\: c=p^2}

\sf{\bullet\:\:\: d=\dfrac{1}{4}}

\bf{\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd}

\sf{\implies p^2\times p^2+p^2\left(-\dfrac{1}{4}\right)+4p^2+4\left(-\dfrac{1}{4}\right)}

\sf{\implies p^2\times p^2-\dfrac{1}{4}p^2+4p^2-4\times \dfrac{1}{4}}

\sf{\implies\displaystyle p^2\times p^2+\frac{15}{4}p^2-4\cdot \frac{1}{4}}

\sf{\implies p^4+\dfrac{15p^2}{4}-1}


Cynefin: Nice :)
Answered by devip649
34

Step-by-step explanation:

\underline{\underline{\sf{\maltese\:\:Question}}}

✠Question

Using suitable identity find \sf{\left(p^2+4\right)\left(p^2-\dfrac{1}{4}\right)}(p

2

+4)(p

2

4

1

)

\underline{\underline{\sf{\maltese\:\:Answer}}}

✠Answer

\bf{p^4+\dfrac{15p^2}{4}-1}p

4

+

4

15p

2

−1

\underline{\underline{\sf{\maltese\:\:Calculations}}}

✠Calculations

Apply FOIL method :

(a + b)(c + d) = ac + ad + bc + bd

We Have :

\sf{\bullet\:\:\: a=p^2}∙a=p

2

\sf{\bullet\:\:\: b=4}∙b=4

\sf{\bullet\:\:\: c=p^2}∙c=p

2

\sf{\bullet\:\:\: d=\dfrac{1}{4}}∙d=

4

1

\bf{\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd}(a+b)(c+d)=ac+ad+bc+bd

\sf{\implies p^2\times p^2+p^2\left(-\dfrac{1}{4}\right)+4p^2+4\left(-\dfrac{1}{4}\right)}⟹p

2

×p

2

+p

2

(−

4

1

)+4p

2

+4(−

4

1

)

\sf{\implies p^2\times p^2-\dfrac{1}{4}p^2+4p^2-4\times \dfrac{1}{4}}⟹p

2

×p

2

4

1

p

2

+4p

2

−4×

4

1

\sf{\implies\displaystyle p^2\times p^2+\frac{15}{4}p^2-4\cdot \frac{1}{4}}⟹p

2

×p

2

+

4

15

p

2

−4⋅

4

1

\sf{\implies p^4+\dfrac{15p^2}{4}-1}⟹p

4

+

4

15p

2

−1

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