The distributive property for the multiplication states that:
[tex]a\cdot(b+c)=a\cdot b+a\cdot c.[/tex](1) Choosing:
• a = (x + 3),
,• b = 4x²,
,• c = 5.
We have:
[tex](x+3)\cdot(4x^2+5)=a\cdot(b+c).[/tex](2) Applying the distributive property for the multiplication, we have:
[tex](x+3)\cdot(4x^2+5)=a\cdot(b+c)=a\cdot b+a\cdot c.[/tex](3) Replacing a = (x + 3), b = 4x² and c = 5, we get:
[tex](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).[/tex]Answer(A)
[tex](x+3)\cdot(4x^2)+(x+3)\cdot(5)[/tex]