Đáp án:
a) $\text{ (x - 2)7($x^{2}$ + 2x - 4) }$
b) $\text{ ($x^{4}$ + 8 - $4.x^{2}$)($x^{4}$ + 8 + $4.x^{2}$) }$
Giải thích các bước giải:
$\text{ a) $7x^{3}$ - 56 }$
$\text{ = $8x^{3}$ - 64 + $x^{3}$ + 8 }$
$\text{ = $(2x)^{3}$ - $4^{3}$ + $x^{3}$ + $2^{3}$ }$
$\text{ = (2x - 4)($4x^{2}$ + 2x.4 + $4^{2}$) + (x + 2)($x^{2}$ + x.2 + $2^{2}$) }$
$\text{ = 2(x - 2)($4x^{2}$ + 2x.4 + $4^{2}$) - (x - 2)($x^{2}$ + x.2 + $2^{2}$) }$
$\text{ = (x - 2)[2.($4x^{2}$ + 2x.4 + $4^{2}$) - ($x^{2}$ + x.2 + $2^{2}$)] }$
$\text{ = (x - 2)[$8x^{2}$ + 16x + $2.4^{2}$ - $x^{2}$ - x.2 - $2^{2}$] }$
$\text{ = (x - 2)($7x^{2}$ + 14x - 28) }$
$\text{ = (x - 2)7($x^{2}$ + 2x - 4) }$
$\text{ b) $x^{8}$ + 64 }$
$\text{ = ($x^{4}$)$^{2}$ + 2.$x^{4}$.8 + $8^{2}$) - 2.$x^{4}$.8 }$
$\text{ = ($x^{4}+8$)$^{2}$ - 16.$x^{4}$ }$
$\text{ = ($x^{4}+8$)$^{2}$ - ($x^{2}.4$)$^{2}$ }$
$\text{ = ($x^{4}$ + 8 - $4.x^{2}$)($x^{4}$ + 8 + $4.x^{2}$) }$
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