QUESTION :-
(2a-5b) (2a + 5b) (4a² +25b²)
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Answers
Step-by-step explanation:
2a−5b)(2a+5b)(4a
2
+25b
2
)
\begin{gathered}\underline{\purple{\frak{ \: \: Find:- \: \: }}} \\ \\ \end{gathered}
Find:−
\sf Value\:of\:(2a-5b)(2a+5b)(4a^2 + 25b^2)Valueof(2a−5b)(2a+5b)(4a
2
+25b
2
)
\begin{gathered}\underline{\purple{\frak{ \: \: Solution:- \: \: }}} \\ \\ \end{gathered}
Solution:−
we, have
\begin{gathered} \dashrightarrow\sf (2a-5b)(2a+5b)(4a^2 + 25b^2) \\ \\ \end{gathered}
⇢(2a−5b)(2a+5b)(4a
2
+25b
2
)
\begin{gathered} \dashrightarrow\sf (2a+5b)(2a - 5b)(4a^2 + 25b^2) \\ \\ \end{gathered}
⇢(2a+5b)(2a−5b)(4a
2
+25b
2
)
\begin{gathered} \dashrightarrow\sf \{(2a)^2 - (5b)^2 \}(4a^2 + 25b^2) \quad \bigg\lgroup\because (a+b)(a-b) = a^2 - b^2\bigg\rgroup \\ \\ \end{gathered}
⇢{(2a)
2
−(5b)
2
}(4a
2
+25b
2
)
⎩
⎪
⎪
⎪
⎧
∵(a+b)(a−b)=a
2
−b
2
⎭
⎪
⎪
⎪
⎫
\begin{gathered} \dashrightarrow\sf (4a^2 - 25b^2)(4a^2 + 25b^2)\\ \\ \end{gathered}
⇢(4a
2
−25b
2
)(4a
2
+25b
2
)
\begin{gathered} \dashrightarrow\sf (4a^2 + 25b^2) (4a^2 - 25b^2) \\ \\ \end{gathered}
⇢(4a
2
+25b
2
)(4a
2
−25b
2
)
\begin{gathered} \dashrightarrow\sf (4a^2)^2 - (25b^2)^2\quad \bigg\lgroup\because (a+b)(a-b) = a^2 - b^2\bigg\rgroup \\ \\ \end{gathered}
⇢(4a
2
)
2
−(25b
2
)
2
⎩
⎪
⎪
⎪
⎧
∵(a+b)(a−b)=a
2
−b
2
⎭
⎪
⎪
⎪
⎫
\begin{gathered} \dashrightarrow\sf 16a^4 - 625b^4 \\ \\ \end{gathered}
⇢16a
4
−625b
4
\underline{\boxed{\sf\therefore (2a-5b)(2a+5b)(4a^2+25b^2) = 16a^4 - 625b^4}}
∴(2a−5b)(2a+5b)(4a
2
+25b
2
)=16a
4
−625b
4
Answer:
(2a-5b) (2a + 5b) (4a² +25b²) = 16a⁴ - 625b⁴
Explanation:
P.F.A the full solution below along with the necessary identities.
Hope you got that.
Thank You.
