Question

Resolve into factors

$1) \: 1 + a + b + c + ab + bc + ca + abc \\ \\ 2) \: abc^{2} + abd^{2} + cda^{2} + cdb^{2}$
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Answer 1

Step-by-step explanation:

Given that:-

1) 1+a+b+c+ab+bc+ca+abc

It can be written as

=>(1+a+c)+(b+ab+bc)+(ca+abc)

=>(1+a+c)+b(1+a+c)+ac(1+b)

=>(1+b)(1+a+c)+ac(1+b)

=>(1+b)(1+a+c+ac)

1+a+b+c+ab+bc+ca+abc=(1+b)(1+a+c+ac)

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2)Given that:-

abc²+abd²+cda²+cdb²

=>(abc²+cda²)+(abd²+cdb²)

=>ac(bc+ad)+bd(ad+bc)

=>ac(bc+ad)+bd(bc+ad)

=>(ac+bd)(bc+ad)

abc²+abd²+cda²+cdb²=(ac+bd)(bc+ad)

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Answer 2

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☃ ƛƝƧƜЄƦ ☃

$\small \pink{{1.) \: 1 + a + b + c + ab + bc + ca + abc}} \\ \small \orange {{ = (1 + a) + b(b+ ab) +( c + ac) + (bc + abc)}} \\ \small \orange{{ = 1(1 + a) + b(1 + a) + c(1 + a) + bc(1 + a)}} \\ \small \orange{{ = (1 + a) \: (1 + b + c + bc) = (1a) \: [ \: 1(1 + b) + c(1 + b)]}} \\ \small \orange{{ = (1 + a) \: (1 + b) \: (1 + c)}}$

$\small \red{{2.) \: abc^{2} + abd^{2} + cda^{2} + cdb^{2}}} \\ \small \blue{{ = (abc^{2} + cda^{2}) + (abd ^{2} + cdb^{2} }} \\ \small \blue{{ = ac(bc + ad) + bd(ad + bc)}} \\ \small \blue{{ = (bc + ad) \: (ac + bd) }}$

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