Question

hola me pueden ayudar con estos ejercicios URGENTE CON TODOS LOS PROCEDIMIENTOS DOY 18 PUNTOS

Answer 1

$(x+y) ^{3} = (x+y) ^{2}*(x+y) = (x^{2} +2xy+y ^{2} )(x+y)=$
$=x^{3} +x^{2}y+2 x^{2} y+2xy^{2}+xy^{2}+y^{3}$
= $x^{3}+3 x^{2} y+3xy^{2} +y ^{3}$

$(a+b) ^{3}= (a+b) ^{2}*(a+b) = (a ^{2}+2ab+b ^{2})(a+b) =$
$=a ^{3}+a ^{2}b+2a ^{2}b+2ab ^{2}+ab ^{2}+b^{3}$
= $a ^{3}+3a ^{2}b+ 3ab ^{2}+b ^{3}$

$(m+n) ^{4}= (m+n) ^{2}*(m+n) ^{2} = (m ^{2}+ 2mn +n ^{2})(m^{2}+2mn+n ^{2})$
= $m ^{4} +2m ^{3}n+m ^{2}+n ^{2}+2m^{3}n+4m ^{2}n ^{2}+2mn^{3}+m ^{2}n ^{2}+2mn ^{3}+n ^{4}$
= $m ^{4} +4m ^{3}n+6m ^{2}n ^{2}+4mn ^{3}+n ^{4}$

$(2x-1)^{4}=(2x-1) ^{2}*(2x-1) ^{2} =$
$(4x^{2} -4x+1)(4 x^{2} -4x+1)=$
$=16 x^{4}-16x^{3}+4 x^{2} -16 x^{3} +16 x^{2} -4x+4 x^{2} -4x+1$
$= 16 x^{4}-32 x^{3} +24 x^{2} -8x+1$

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(2a-1)(1+2a) = 2a + 4a²-1-2a = 4a² - 1

(1-3ax)(3ax +1) = 3ax+1-9a²x²-3ax = 1 - 9a²x²

(x+y-2) (x-y+2) = x² -xy+2x+ xy -y²+2y-2x +2y-4 = x² - y² + 4y - 4