Question

expand:(x+3)(x+5)(x+2)

Answer 1

Answer:

(x + 3)(x + 5)(x + 2)

First let's distribute ( x + 3) over ( x + 5 )

⇛ x(x + 5) + 3(x + 5)[ ( x + 2 )]

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

⇛ ( x² + 5x + 3x + 15 )( x + 2 )

Combining like terms

⇛ ( x² + 8x + 15 )( x + 2 )

Distributing ( x + 2 ) over the first term

⇛ x(x² + 8x + 15) + 2(x² + 8x + 15 )

⇛ x(x²) + x(8x) + x(15) + 2(x² + 8x + 15 )

⇛ x³ + 8x² + 15x + 2(x² + 8x + 15 )

⇛ x³ + 8x² + 15x + 2(x²) + 2(8x) + 2(15 )  

⇛ x³ + 8x² + 15x + 2x² + 16x + 30

Combining like terms

⇛ x³ ( 8 + 2)x² + (15 + 16)x + 30

⇛ x³ + 10x² + 31x + 30

Hope it helps you :)

Answer 2

Given,

$(x+3)(x+5)(x+2)$

W have to expand the given expression,

• Distribution property of multiplication: The distribution property of multiplication states that multiplying two factors together gives the same result as breaking one factor up into two addends, multiplying both addends with the remaining factor, then adding both products together.

Now,

$(x+3)(x+5)(x+2)$

$(x(x+5)+3(x+5))(x+2)$

$= (x^{2} +5x+3x+15)(x+2)$

$=(x^{2} +8x+15)(x+2)$

$= x(x^{2} +8x+15)+2(x^{2} +8x+15)$

$=x^{3}+8x^{2} +15x+2x^{2} +16x+30$

$=x^{3}+10x^{2} +31x+30$

Therefore, the answer is $x^{3}+10x^{2} +31x+30$.