Suman Cole

2020-12-05

Solve. Factor each expression.

a.${x}^{3}+216$

a.

Asma Vang

Skilled2020-12-06Added 93 answers

Calculation:

Consider the polynomial as,

${x}^{3}+216$

Rewrite the polynomial as,

${x}^{3}+216={x}^{3}+{6}^{3}$

According to the factorized form of the sum of two cubes,${u}^{3}+{v}^{3}=(u+v)({u}^{2}\u2014uv+{v}^{2})$ .

${x}^{3}+216={3}^{3}+{6}^{3}$

$=(x+6)[{x}^{2}-x(6)+{6}^{2}]$

$=(x+6)({x}^{2}\u20146x+36)$

Therefore, the factorization of the polynomial${x}^{3}+216$ is $(x+6)({x}^{2}\u20146x+36)$ .

Consider the polynomial as,

Rewrite the polynomial as,

According to the factorized form of the sum of two cubes,

Therefore, the factorization of the polynomial

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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