Question

Expand (x+3) (x+5) (x+2).



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Answer 1

Answer:

Step-by-step explanation:

= [(x+3)(x+5)] (x+2)

applying identity (x+a) (x+b)= x^2 +(a+b)x +ab

= [ x^2+(3+5)x + 3*5] (x+2)

=[x^2 + 8x +15] (x+2)

=x[ x^2 +8x+15 ] +2[x^2+8x +15]

=x^3 + 8x^2 +15x +2x^2+ 16x +30

= x^3 + 10x^2 + 31x +30

Answer 2

• (x + 3) (x + 5) (x + 2) = x³ + 10x² + 31x + 30

Step-by-step explanation:

Given,

• (x + 3) (x + 5) (x + 2)

Comparing,

• (x + a) (x + b) (x + c) = (x + 3) (x + 5) (x + 2)

we get,

• x = x
• a = 3
• b = 5
• c = 2

Solving,

⟼ (x + a) (x + b) (x + c) = x³ + (a + b + c) x² + (ab + bc + ca) x + abc

⟼ (x + 3) (x + 5) (x + 2) = (x)³ + (3 + 5 + 2) (x)² + (ab + bc + ca) x + abc

⟼ (x + 3) (x + 5) (x + 2) = x³ + 10x² + [(3 × 5) + (5 × 2) + (2 × 3)] x + (5 × 3 × 2)

⟼ (x + 3) (x + 5) (x + 2) = x³ + 10x² + [(15) + (10) + (6)] x + (5 × 3 × 2)

⟼ (x + 3) (x + 5) (x + 2) = x³ + 10x² + 31x + 30

• The expanded form = (x + 3) (x + 5) (x + 2) = x³ + 10x² + 31x + 30