Write in Standard Form y=(2x+3)(x-1)(x-4)

$y = (2 x + 3) (x - 1) (x - 4)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$y = a x^{2} + b x + c$

Step 2

Expand $(2 x + 3) (x - 1)$ using the FOIL Method.

Apply the distributive property.

$y = (2 x (x - 1) + 3 (x - 1)) (x - 4)$

Apply the distributive property.

$y = (2 x \cdot x + 2 x \cdot - 1 + 3 (x - 1)) (x - 4)$

Apply the distributive property.

$y = (2 x \cdot x + 2 x \cdot - 1 + 3 x + 3 \cdot - 1) (x - 4)$

Step 3

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$y = (2 (x \cdot x) + 2 x \cdot - 1 + 3 x + 3 \cdot - 1) (x - 4)$

Multiply $x$ by $x$ .

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

Multiply $- 1$ by $2$ .

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

Multiply $3$ by $- 1$ .

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

Add $- 2 x$ and $3 x$ .

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

Step 4

Expand $(2 x^{2} + x - 3) (x - 4)$ by multiplying each term in the first expression by each term in the second expression.

$y = 2 x^{2} x + 2 x^{2} \cdot - 4 + x \cdot x + x \cdot - 4 - 3 x - 3 \cdot - 4$

Step 5

Simplify terms.

Simplify each term.

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

$y = 2 x^{3} + 2 x^{2} \cdot - 4 + x \cdot x + x \cdot - 4 - 3 x - 3 \cdot - 4$

Multiply $- 4$ by $2$ .

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

Multiply $x$ by $x$ .

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

Move $- 4$ to the left of $x$ .

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

Multiply $- 3$ by $- 4$ .

$y = 2 x^{3} - 8 x^{2} + x^{2} - 4 x - 3 x + 12$

Simplify by adding terms.

Add $- 8 x^{2}$ and $x^{2}$ .

$y = 2 x^{3} - 7 x^{2} - 4 x - 3 x + 12$

Subtract $3 x$ from $- 4 x$ .

$y = 2 x^{3} - 7 x^{2} - 7 x + 12$

Step 6

Write in Standard Form y=(2x+3)(x-1)(x-4)

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