Algebra Examples

$y = {(4 x + 3)}^{2} - 24 x$

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.

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Step 2.1

Rewrite ${(4 x + 3)}^{2}$ as $(4 x + 3) (4 x + 3)$ .

$y = (4 x + 3) (4 x + 3) - 24 x$

Step 2.2

Expand $(4 x + 3) (4 x + 3)$ using the FOIL Method.

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Step 2.2.1

Apply the distributive property.

$y = 4 x (4 x + 3) + 3 (4 x + 3) - 24 x$

Step 2.2.2

Apply the distributive property.

$y = 4 x (4 x) + 4 x \cdot 3 + 3 (4 x + 3) - 24 x$

Step 2.2.3

Apply the distributive property.

$y = 4 x (4 x) + 4 x \cdot 3 + 3 (4 x) + 3 \cdot 3 - 24 x$

Step 2.3

Simplify and combine like terms.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Rewrite using the commutative property of multiplication.

$y = 4 \cdot (4 x \cdot x) + 4 x \cdot 3 + 3 (4 x) + 3 \cdot 3 - 24 x$

Step 2.3.1.2

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

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Step 2.3.1.2.1

Move $x$ .

$y = 4 \cdot (4 (x \cdot x)) + 4 x \cdot 3 + 3 (4 x) + 3 \cdot 3 - 24 x$

Step 2.3.1.2.2

Multiply $x$ by $x$ .

$y = 4 \cdot (4 x^{2}) + 4 x \cdot 3 + 3 (4 x) + 3 \cdot 3 - 24 x$

Step 2.3.1.3

Multiply $4$ by $4$ .

$y = 16 x^{2} + 4 x \cdot 3 + 3 (4 x) + 3 \cdot 3 - 24 x$

Step 2.3.1.4

Multiply $3$ by $4$ .

$y = 16 x^{2} + 12 x + 3 (4 x) + 3 \cdot 3 - 24 x$

Step 2.3.1.5

Multiply $4$ by $3$ .

$y = 16 x^{2} + 12 x + 12 x + 3 \cdot 3 - 24 x$

Step 2.3.1.6

Multiply $3$ by $3$ .

$y = 16 x^{2} + 12 x + 12 x + 9 - 24 x$

Step 2.3.2

Add $12 x$ and $12 x$ .

$y = 16 x^{2} + 24 x + 9 - 24 x$

Step 3

Combine the opposite terms in $16 x^{2} + 24 x + 9 - 24 x$ .

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Step 3.1

Subtract $24 x$ from $24 x$ .

$y = 16 x^{2} + 0 + 9$

Step 3.2

Add $16 x^{2}$ and $0$ .

$y = 16 x^{2} + 9$

Step 4