Find the Product f(x)=2x , g(x)=x^2+2 , h(x)=-4x+3

$f (x) = 2 x$ , $g (x) = x^{2} + 2$ , $h (x) = - 4 x + 3$

Step 1

Replace the function designators with the actual functions in $f (x) \cdot (g (x)) \cdot (h (x))$ .

$(2 x) \cdot (x^{2} + 2) \cdot (- 4 x + 3)$

Step 2

Simplify.

Apply the distributive property.

$(2 x \cdot x^{2} + 2 x \cdot 2) \cdot (- 4 x + 3)$

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$(2 (x^{2} x) + 2 x \cdot 2) \cdot (- 4 x + 3)$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$(2 (x^{2} x^{1}) + 2 x \cdot 2) \cdot (- 4 x + 3)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(2 x^{2 + 1} + 2 x \cdot 2) \cdot (- 4 x + 3)$

Add $2$ and $1$ .

$(2 x^{3} + 2 x \cdot 2) \cdot (- 4 x + 3)$

Multiply $2$ by $2$ .

$(2 x^{3} + 4 x) \cdot (- 4 x + 3)$

Expand $(2 x^{3} + 4 x) (- 4 x + 3)$ using the FOIL Method.

Apply the distributive property.

$2 x^{3} (- 4 x + 3) + 4 x (- 4 x + 3)$

Apply the distributive property.

$2 x^{3} (- 4 x) + 2 x^{3} \cdot 3 + 4 x (- 4 x + 3)$

Apply the distributive property.

$2 x^{3} (- 4 x) + 2 x^{3} \cdot 3 + 4 x (- 4 x) + 4 x \cdot 3$

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot - 4 x^{3} x + 2 x^{3} \cdot 3 + 4 x (- 4 x) + 4 x \cdot 3$

Multiply $x^{3}$ by $x$ by adding the exponents.

Move $x$ .

$2 \cdot - 4 (x \cdot x^{3}) + 2 x^{3} \cdot 3 + 4 x (- 4 x) + 4 x \cdot 3$

Multiply $x$ by $x^{3}$ .

Raise $x$ to the power of $1$ .

$2 \cdot - 4 (x^{1} x^{3}) + 2 x^{3} \cdot 3 + 4 x (- 4 x) + 4 x \cdot 3$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 \cdot - 4 x^{1 + 3} + 2 x^{3} \cdot 3 + 4 x (- 4 x) + 4 x \cdot 3$

Add $1$ and $3$ .

$2 \cdot - 4 x^{4} + 2 x^{3} \cdot 3 + 4 x (- 4 x) + 4 x \cdot 3$

Multiply $2$ by $- 4$ .

$- 8 x^{4} + 2 x^{3} \cdot 3 + 4 x (- 4 x) + 4 x \cdot 3$

Multiply $3$ by $2$ .

$- 8 x^{4} + 6 x^{3} + 4 x (- 4 x) + 4 x \cdot 3$

Rewrite using the commutative property of multiplication.

$- 8 x^{4} + 6 x^{3} + 4 \cdot - 4 x \cdot x + 4 x \cdot 3$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$- 8 x^{4} + 6 x^{3} + 4 \cdot - 4 (x \cdot x) + 4 x \cdot 3$

Multiply $x$ by $x$ .

$- 8 x^{4} + 6 x^{3} + 4 \cdot - 4 x^{2} + 4 x \cdot 3$

Multiply $4$ by $- 4$ .

$- 8 x^{4} + 6 x^{3} - 16 x^{2} + 4 x \cdot 3$

Multiply $3$ by $4$ .

$- 8 x^{4} + 6 x^{3} - 16 x^{2} + 12 x$

Find the Product f(x)=2x , g(x)=x^2+2 , h(x)=-4x+3

Related Questions

Support LCMGCF.com by disabling your adblocker.