Using suitable identity find
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Answers
- Using suitable identity find
Apply FOIL method :
- (a + b)(c + d) = ac + ad + bc + bd
We Have :
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