Write in Standard Form y=(x-5)(x+5)(2x-1)

$y = (x - 5) (x + 5) (2 x - 1)$

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 $(x - 5) (x + 5)$ using the FOIL Method.

Apply the distributive property.

$y = (x (x + 5) - 5 (x + 5)) (2 x - 1)$

Apply the distributive property.

$y = (x \cdot x + x \cdot 5 - 5 (x + 5)) (2 x - 1)$

Apply the distributive property.

$y = (x \cdot x + x \cdot 5 - 5 x - 5 \cdot 5) (2 x - 1)$

Step 3

Simplify terms.

Combine the opposite terms in $x \cdot x + x \cdot 5 - 5 x - 5 \cdot 5$ .

Reorder the factors in the terms $x \cdot 5$ and $- 5 x$ .

$y = (x \cdot x + 5 x - 5 x - 5 \cdot 5) (2 x - 1)$

Subtract $5 x$ from $5 x$ .

$y = (x \cdot x + 0 - 5 \cdot 5) (2 x - 1)$

Add $x \cdot x$ and $0$ .

$y = (x \cdot x - 5 \cdot 5) (2 x - 1)$

Simplify each term.

Multiply $x$ by $x$ .

$y = (x^{2} - 5 \cdot 5) (2 x - 1)$

Multiply $- 5$ by $5$ .

$y = (x^{2} - 25) (2 x - 1)$

Step 4

Expand $(x^{2} - 25) (2 x - 1)$ using the FOIL Method.

Apply the distributive property.

$y = x^{2} (2 x - 1) - 25 (2 x - 1)$

Apply the distributive property.

$y = x^{2} (2 x) + x^{2} \cdot - 1 - 25 (2 x - 1)$

Apply the distributive property.

$y = x^{2} (2 x) + x^{2} \cdot - 1 - 25 (2 x) - 25 \cdot - 1$

Step 5

Simplify each term.

Rewrite using the commutative property of multiplication.

$y = 2 x^{2} x + x^{2} \cdot - 1 - 25 (2 x) - 25 \cdot - 1$

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

Move $x$ .

$y = 2 (x \cdot x^{2}) + x^{2} \cdot - 1 - 25 (2 x) - 25 \cdot - 1$

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

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

$y = 2 (x \cdot x^{2}) + x^{2} \cdot - 1 - 25 (2 x) - 25 \cdot - 1$

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

$y = 2 x^{1 + 2} + x^{2} \cdot - 1 - 25 (2 x) - 25 \cdot - 1$

Add $1$ and $2$ .

$y = 2 x^{3} + x^{2} \cdot - 1 - 25 (2 x) - 25 \cdot - 1$

Move $- 1$ to the left of $x^{2}$ .

$y = 2 x^{3} - 1 \cdot x^{2} - 25 (2 x) - 25 \cdot - 1$

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

$y = 2 x^{3} - x^{2} - 25 (2 x) - 25 \cdot - 1$

Multiply $2$ by $- 25$ .

$y = 2 x^{3} - x^{2} - 50 x - 25 \cdot - 1$

Multiply $- 25$ by $- 1$ .

$y = 2 x^{3} - x^{2} - 50 x + 25$

Step 6

Write in Standard Form y=(x-5)(x+5)(2x-1)

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