# How do you factor # 27x^3 + 54 x^2 + 36x +8# by grouping?

Note that the first and last terms are perfect cubes and find:

#27x^3+54x^2+36x+8 = (3x+2)^3#

Notice that the ratio between the first and second coefficients is not the same as that between the third and fourth.

So this does not factor by grouping.

Yes - that's our factoring.

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To factor 27x^3 + 54x^2 + 36x + 8 by grouping:

Step 1: Group the terms: (27x^3 + 54x^2) + (36x + 8)

Step 2: Factor out the greatest common factor from each group: 27x^2(x + 2) + 4(9x + 2)

Step 3: Notice that both groups have a common factor of (x + 2): (x + 2)(27x^2 + 4(9x + 2))

Step 4: Simplify: (x + 2)(27x^2 + 36x + 8)

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To factor the expression (27x^3 + 54x^2 + 36x + 8) by grouping, follow these steps:

Step 1: Group the terms in pairs:

( (27x^3 + 54x^2) + (36x + 8) )

Step 2: Factor out the greatest common factor (GCF) from each pair:

( 27x^2(x + 2) + 4(9x + 2) )

Step 3: Notice that both terms now have a common factor of ( (x + 2) ), so factor it out:

( (x + 2)(27x^2 + 4) )

This is the factored form of the expression ( 27x^3 + 54x^2 + 36x + 8 ) by grouping.

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