Question

Factorise. i) m square +8mn +15n square. ii)p square - 26p +133 iii) x square -8x -105 iv)x square +15x -154. v) x to the power 4 -x square -12
plzzz guys jldi answer do !! ​

Answer 1

Solutions:-

$i) {m}^{2} + 8mn + 15n$

$= {m}^{2} + (3 + 5)mn + 15n$

$= {m}^{2} + 3mn + 5mn + 15n$

$= m(m + 3n) + 5n(m + 3n)$

$= (m + 5n)(m + 3n)$

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${p}^{2} - 26p + 133$

$= {p}^{2} - (17 + 9)p + 133$

$= {p}^{2} - 17p - 9p + 133$

$= p(p - 17) - 9(p - 17)$

$= (p - 9)(p - 17)$

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${x}^{2} - 8x - 105$

$= {x}^{2} - (15 - 7)x - 105$

$= {x}^{2} - 15x + 7x - 105$

$= x(x - 15) + 7(x - 15)$

$= (x + 7)(x - 15)$

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${x}^{2} + 15x - 154$

$= {x}^{2} + (22 - 7)x - 154$

$= {x}^{2} + 22x - 7x - 154$

$= x(x + 22) - 7(x + 22)$

$= (x - 7)(x + 22)$

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${x}^{4} - {x}^{2} - 12$

$= { ({x}^{2}) }^{2} - {x}^{2} - 12$

$= ( {x}^{2} - 4)( {x}^{2} - 3)$

$= ({x}^{2} - {2}^{2} )( {x}^{2} - 3)$

$= (x - 2)(x + 2)( {x}^{2} - 3)$

Answer 2

1) m² + 8mn + 15n²

The above equation is in the form ax² + bx + c. So, we have to find it's factor.

We have to find the numbers whose sum is b and product is c.

=> m² + 3mn + 5mn + 15n²

=> m(m + 3n) + 5n(m + 3n)

=> (m + 5n) (m + 3n)

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2) p² - 26p + 153

=> p² - 17p - 9p + 153

=> p(p - 17) - 9(p - 17)

=> (p - 17) (p - 9)

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3) x² - 8x - 105

=> x² - 15x + 7x - 105

=> x(x - 15) + 7(x - 15)

=> (x - 15) (x + 7)

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4) x² + 15x - 154

=> x² + 22x - 7x - 154

=> x(x + 22) - 7(x + 22)

=> (x - 7) (x + 22)

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5) x⁴ - x² - 12

=> x⁴ - 4x² + 3x² - 12

=> x²(x² - 4) + 3(x² - 4)

=> (x² + 3) (x² - 4)

=> (x² + 3) [(x)² - (2)²]

(a + b) (a - b) = a² - b²

=> (x² + 3) (x - 2) (x + 2)

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