Write in Standard Form y=2(2x-5)^2-10

$y = 2 {(2 x - 5)}^{2} - 10$

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

Simplify each term.

Rewrite ${(2 x - 5)}^{2}$ as $(2 x - 5) (2 x - 5)$ .

$y = 2 ((2 x - 5) (2 x - 5)) - 10$

Expand $(2 x - 5) (2 x - 5)$ using the FOIL Method.

Apply the distributive property.

$y = 2 (2 x (2 x - 5) - 5 (2 x - 5)) - 10$

Apply the distributive property.

$y = 2 (2 x (2 x) + 2 x \cdot - 5 - 5 (2 x - 5)) - 10$

Apply the distributive property.

$y = 2 (2 x (2 x) + 2 x \cdot - 5 - 5 (2 x) - 5 \cdot - 5) - 10$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$y = 2 (2 \cdot (2 x \cdot x) + 2 x \cdot - 5 - 5 (2 x) - 5 \cdot - 5) - 10$

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

Move $x$ .

$y = 2 (2 \cdot (2 (x \cdot x)) + 2 x \cdot - 5 - 5 (2 x) - 5 \cdot - 5) - 10$

Multiply $x$ by $x$ .

$y = 2 (2 \cdot (2 x^{2}) + 2 x \cdot - 5 - 5 (2 x) - 5 \cdot - 5) - 10$

Multiply $2$ by $2$ .

$y = 2 (4 x^{2} + 2 x \cdot - 5 - 5 (2 x) - 5 \cdot - 5) - 10$

Multiply $- 5$ by $2$ .

$y = 2 (4 x^{2} - 10 x - 5 (2 x) - 5 \cdot - 5) - 10$

Multiply $2$ by $- 5$ .

$y = 2 (4 x^{2} - 10 x - 10 x - 5 \cdot - 5) - 10$

Multiply $- 5$ by $- 5$ .

$y = 2 (4 x^{2} - 10 x - 10 x + 25) - 10$

Subtract $10 x$ from $- 10 x$ .

$y = 2 (4 x^{2} - 20 x + 25) - 10$

Apply the distributive property.

$y = 2 (4 x^{2}) + 2 (- 20 x) + 2 \cdot 25 - 10$

Simplify.

Multiply $4$ by $2$ .

$y = 8 x^{2} + 2 (- 20 x) + 2 \cdot 25 - 10$

Multiply $- 20$ by $2$ .

$y = 8 x^{2} - 40 x + 2 \cdot 25 - 10$

Multiply $2$ by $25$ .

$y = 8 x^{2} - 40 x + 50 - 10$

Step 3

Subtract $10$ from $50$ .

$y = 8 x^{2} - 40 x + 40$

Step 4

Write in Standard Form y=2(2x-5)^2-10

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