Answer:

5a-3a-8

2a-8=0

2a=8

a=4

Verified answer

Appropriate Question: Factorise

[tex]\sf \: 5 {( {5x}^{2} - 3x) }^{2} - 3( {5x}^{2} - 3x) - 8 \\ \\ [/tex]

Answer:

[tex]\sf \: \boxed{\sf \: \: ({25x}^{2} - 15x - 8)({5x}^{2} - 3x + 1) \: } \\ \\ [/tex]

Step-by-step explanation:

Given expression is

[tex]\sf \: 5 {( {5x}^{2} - 3x) }^{2} - 3( {5x}^{2} - 3x) - 8 \\ \\ [/tex]

Let assume that

[tex]\sf \: {5x}^{2} - 3x = a \\ \\ [/tex]

So, above expression can be rewritten as

[tex]\sf \: = \: 5 {a}^{2} - 3a - 8 \\ \\ [/tex]

On splitting the middle terms, we get

[tex]\sf \: = \: 5 {a}^{2} - 8a + 5a - 8 \\ \\ [/tex]

[tex]\sf \: = \: a(5a - 8) + 1(5a - 8) \\ \\ [/tex]

[tex]\sf \: = \: (5a - 8)(a + 1) \\ \\ [/tex]

On substituting the value of a, we get

[tex]\sf \: = \: [ 5( {5x}^{2} - 3x) - 8]({5x}^{2} - 3x + 1) \\ \\ [/tex]

[tex]\sf \: = \: ({25x}^{2} - 15x - 8)({5x}^{2} - 3x + 1) \\ \\ [/tex]

[tex]\rule{190pt}{2pt}[/tex]

Additional Information

[tex]\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{{More \: identities}}}} \\ \\ \bigstar \: \bf{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \bigstar \: \bf{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \bigstar \: \bf{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \end{array} }}\end{gathered}\end{gathered}\end{gathered}[/tex]