Question

I need help figuring out which of these four options is equivalent to$(x + 3)(4 {x}^{2} + 5)$

Answer 1

Explanation

The distributive property for the multiplication states that:

$a\cdot(b+c)=a\cdot b+a\cdot c.$

(1) Choosing:

• a = (x + 3),

,

• b = 4x²,

,

• c = 5.

We have:

$(x+3)\cdot(4x^2+5)=a\cdot(b+c).$

(2) Applying the distributive property for the multiplication, we have:

$(x+3)\cdot(4x^2+5)=a\cdot(b+c)=a\cdot b+a\cdot c.$

(3) Replacing a = (x + 3), b = 4x² and c = 5, we get:

$(x+3)\cdot(4x^2+5)=a\cdot(b+c)=a\cdot b+a\cdot c=(x+3)\cdot(4x^2)+(x+3)\cdot(5).$Answer

(A)

$(x+3)\cdot(4x^2)+(x+3)\cdot(5)$