Write as an Equation m(x)=(3x-1)(3-x)+4x^2+19

$m (x) = (3 x - 1) (3 - x) + 4 x^{2} + 19$

Step 1

Rewrite the function as an equation.

$y = (3 x - 1) (3 - x) + 4 x^{2} + 19$

Step 2

Simplify $(3 x - 1) (3 - x) + 4 x^{2} + 19$ .

Simplify each term.

Expand $(3 x - 1) (3 - x)$ using the FOIL Method.

Apply the distributive property.

$y = 3 x (3 - x) - 1 (3 - x) + 4 x^{2} + 19$

Apply the distributive property.

$y = 3 x \cdot 3 + 3 x (- x) - 1 (3 - x) + 4 x^{2} + 19$

Apply the distributive property.

$y = 3 x \cdot 3 + 3 x (- x) - 1 \cdot 3 - 1 (- x) + 4 x^{2} + 19$

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $3$ .

$y = 9 x + 3 x (- x) - 1 \cdot 3 - 1 (- x) + 4 x^{2} + 19$

Rewrite using the commutative property of multiplication.

$y = 9 x + 3 \cdot - 1 x \cdot x - 1 \cdot 3 - 1 (- x) + 4 x^{2} + 19$

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

Move $x$ .

$y = 9 x + 3 \cdot - 1 (x \cdot x) - 1 \cdot 3 - 1 (- x) + 4 x^{2} + 19$

Multiply $x$ by $x$ .

$y = 9 x + 3 \cdot - 1 x^{2} - 1 \cdot 3 - 1 (- x) + 4 x^{2} + 19$

Multiply $3$ by $- 1$ .

$y = 9 x - 3 x^{2} - 1 \cdot 3 - 1 (- x) + 4 x^{2} + 19$

Multiply $- 1$ by $3$ .

$y = 9 x - 3 x^{2} - 3 - 1 (- x) + 4 x^{2} + 19$

Multiply $- 1 (- x)$ .

Multiply $- 1$ by $- 1$ .

$y = 9 x - 3 x^{2} - 3 + 1 x + 4 x^{2} + 19$

Multiply $x$ by $1$ .

$y = 9 x - 3 x^{2} - 3 + x + 4 x^{2} + 19$

Add $9 x$ and $x$ .

$y = 10 x - 3 x^{2} - 3 + 4 x^{2} + 19$

Simplify by adding terms.

Add $- 3 x^{2}$ and $4 x^{2}$ .

$y = 10 x + x^{2} - 3 + 19$

Simplify the expression.

Add $- 3$ and $19$ .

$y = 10 x + x^{2} + 16$

Reorder $10 x$ and $x^{2}$ .

$y = x^{2} + 10 x + 16$