Question

Factorise m^3+m
Factorise 25-y^2
Factorise x^2+3x-28

Answer 1

1. m³ + m

= m( m² + 1) [ a² + b²]

= (a-b)² + 2ab

= m { (m –1)² + 2× m × 1 }

= m { ( m–1)² + 2m}

2. 25 – y² [ a² – b²]

= 5² – y²

= (5+y) (5–y)

3. x² + 3x –28 [ middle term factorisation]

= x² + 7x –4x –28

= x( x +7) –4 ( x + 7 )

= ( x–4) (x+7)

Answer 2

➊ Factorise :-
`\sf{m^(3) + m}`

Solution :-

`→ \ \ \sf\purple{m^(3) + m}`

• Factor out m from the expression

`→\:\:\bf\red{ m * (m^(2) + 1)}`

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➋ Factorise :-
`\sf{25-y^(2)}`

Solution :-

`→\:\:\sf\purple{25-y^(2)}`

• Write the number in the exponential form with an exponent of 2

`→\:\:\sf\green{5^(2) - y^(2)}`

• Using a²-b² = (a-b)(a+b), factor the expression

`→\:\:\bf\red{(5-y)* (5+y)}`

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➌ Factorise :-
`\sf{x^(2)+3x - 28}`

Solution :-

`→\:\:\sf\purple{x^(2)+3x - 28}`

• Rewrite 3x as a difference

`→\:\:\sf\green{x^(2)+7x-4x-28}`

• Factor the expressions

`→\:\:\sf\orange{x * (x +7) -4 (x+7)}`

• Factor out x + 7 from the expression

`→\:\:\bf\red{(x + 7)* (x - 4)}`