Respuesta :
We want to find the product:
[tex]\displaystyle{ 2x^4\cdot(4x^2 + 3x + 1)[/tex].
By the [tex]\text{Distributive property}[/tex], we distribute [tex]2x^4[/tex] over each of the three terms inside the parenthesis:
[tex]\displaystyle{ 2x^4\cdot(4x^2 + 3x + 1)=2x^4\cdot4x^2+2x^4\cdot3x+2x^4\cdot1[/tex].
Multiplying the coefficients, and adding the exponents we get:
[tex]8x^6+6x^5+2x^4[/tex].
Answer: [tex]8x^6+6x^5+2x^4[/tex].
[tex]\displaystyle{ 2x^4\cdot(4x^2 + 3x + 1)[/tex].
By the [tex]\text{Distributive property}[/tex], we distribute [tex]2x^4[/tex] over each of the three terms inside the parenthesis:
[tex]\displaystyle{ 2x^4\cdot(4x^2 + 3x + 1)=2x^4\cdot4x^2+2x^4\cdot3x+2x^4\cdot1[/tex].
Multiplying the coefficients, and adding the exponents we get:
[tex]8x^6+6x^5+2x^4[/tex].
Answer: [tex]8x^6+6x^5+2x^4[/tex].
In mathematics, the distributive property is a property that allows us to multiply a mathematical expression by a sum. It states that if A, B, and C are mathematical expressions, then A(B + C) = AB + AC. This property comes in extremely handy in many different problems and applications in mathematics.
[tex] = \displaystyle{ {2x}^{4} (4 {x}^{2} + 3x + 1) }[/tex]
[tex] = (2 \times 4)x {}^{(4 + 2)} + (2 \times 3)x {}^{4 + 1} + (2 \times 1) {x}^{4} [/tex]
[tex] = 8 {x}^{6} + {6x}^{5} + {2x}^{4} [/tex]
