Question

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

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

• 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 :

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

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

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

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

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

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

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

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

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

Answer 2

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