Question

find LCM and HCF of:
x^4+(2b^2-a^2)x^2 , x^4+2ax^3+a^2x^2-b^4​

Answer 1

Answer:

Take mate

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

((x4) - 2x3a) + x2a2

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

x4 - 2x3a + x2a2 = x2 • (x2 - 2xa + a2)

Trying to factor a multi variable polynomial :

3.2 Factoring x2 - 2xa + a2

Try to factor this multi-variable trinomial using trial and error

Found a factorization : (x - a)•(x - a)

Detecting a perfect square :

3.3 x2 -2xa +a2 is a perfect square

It factors into (x-a)•(x-a)

which is another way of writing (x-a)2

Answer 2

Step-by-step explanation:

${x}^{4} + (2 {b}^{2} - {a}^{2} ) {x}^{2} + {b}^{4} \\ ({x}^{2} {)}^{2} + ( {b}^{2} {)}^{2} + 2 {x}^{2} {b}^{2} - {a}^{2} {x}^{2} \\ ( {x}^{2} + {b}^{2} {)}^{2} - (ax {)}^{2} \\ ( {x}^{2} + ax + {b}^{2} )( {x}^{2} - ax + {b}^{2} )$

again

${x}^{4} + 2a {x}^{3} + {a}^{2} {x}^{2} - {b}^{4} \\ {x}^{2} ( {x}^{2} + 2ax + {a}^{2} ) - {b}^{4} \\ {x}^{2} (x + a {)}^{2} - {b}^{4} \\ (x(x + a) {)}^{2} - ( {b}^{2} {)}^{2} \\ ( {x}^{2} + ax {)}^{2} - ( {b}^{2} {)}^{2} \\ ( {x}^{2} + ax + {b}^{2} )( {x}^{2} + ax - {b}^{2} )$

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