Question

16p^4-q^4 factories ​

Answer 1

♣ɢɪᴠᴇɴ:–

$\large \tt{16p^4-q^4}$

♣ᴛᴏ ғɪɴᴅ:–

Factories the given equation

♣sᴏʟᴜᴛɪᴏɴ:–

$\qquad \quad : \longrightarrow\tt{16 {p}^{4} - 81 {q}^{4}}$

$\qquad \quad: \longrightarrow \tt{{(4 {p}^{2}) }^{2} - {(9 {q}^{2}) }^{2}}$

We will use one identity,that is :–

$\quad \bull \quad \tt{ {a}^{2} - {b}^{2} = (a - b)(a + b)}$

$\qquad \quad : \longrightarrow\tt{(4 {p}^{2} - 9 {q}^{2} )(4 {p}^{2} + 9 {y}^{2} )}$

$\qquad \quad : \longrightarrow \tt{ {((2 {p}^{2}) - (3 {q}^{2} ))}(4 {p}^{2} + 9 {q}^{2} )}$

$\qquad \quad : \longrightarrow \underline{\boxed{\tt{ (2p - 3q)(2p - 3q)(4 {p}^{2} + 9 {q}^{2})}} }$

Answer 2

♣ɢɪᴠᴇɴ:–

\large \tt{16p^4-q^4}16p

4

−q

4

♣ᴛᴏ ғɪɴᴅ:–

Factories the given equation

♣sᴏʟᴜᴛɪᴏɴ:–

\qquad \quad : \longrightarrow\tt{16 {p}^{4} - 81 {q}^{4}}:⟶16p

4

−81q

4

\qquad \quad: \longrightarrow \tt{{(4 {p}^{2}) }^{2} - {(9 {q}^{2}) }^{2}}:⟶(4p

2

)

2

−(9q

2

)

2

We will use one identity,that is :–

\quad \bull \quad \tt{ {a}^{2} - {b}^{2} = (a - b)(a + b)}∙a

2

−b

2

=(a−b)(a+b)

\begin{gathered} \qquad \quad : \longrightarrow\tt{(4 {p}^{2} - 9 {q}^{2} )(4 {p}^{2} + 9 {y}^{2} )}\\\end{gathered}

:⟶(4p

2

−9q

2

)(4p

2

+9y

2

)

\begin{gathered} \qquad \quad : \longrightarrow \tt{ {((2 {p}^{2}) - (3 {q}^{2} ))}(4 {p}^{2} + 9 {q}^{2} )} \\\end{gathered}

:⟶((2p

2

)−(3q

2

))(4p

2

+9q

2

)

\begin{gathered} \qquad \quad : \longrightarrow \underline{\boxed{\tt{ (2p - 3q)(2p - 3q)(4 {p}^{2} + 9 {q}^{2})}} }\\\end{gathered}

:⟶

(2p−3q)(2p−3q)(4p

2

+9q

2

)