Precalculus Examples

$3 a (- a + 5) - 4 {(2 a - 3)}^{2} - a (a - 1)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 a (- a) + 3 a \cdot 5 - 4 {(2 a - 3)}^{2} - a (a - 1)$

Step 1.2

Rewrite using the commutative property of multiplication.

$3 \cdot - 1 a \cdot a + 3 a \cdot 5 - 4 {(2 a - 3)}^{2} - a (a - 1)$

Step 1.3

Multiply $5$ by $3$ .

$3 \cdot - 1 a \cdot a + 15 a - 4 {(2 a - 3)}^{2} - a (a - 1)$

Step 1.4

Simplify each term.

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Step 1.4.1

Multiply $a$ by $a$ by adding the exponents.

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Step 1.4.1.1

Move $a$ .

$3 \cdot - 1 (a \cdot a) + 15 a - 4 {(2 a - 3)}^{2} - a (a - 1)$

Step 1.4.1.2

Multiply $a$ by $a$ .

$3 \cdot - 1 a^{2} + 15 a - 4 {(2 a - 3)}^{2} - a (a - 1)$

Step 1.4.2

Multiply $3$ by $- 1$ .

$- 3 a^{2} + 15 a - 4 {(2 a - 3)}^{2} - a (a - 1)$

Step 1.5

Rewrite ${(2 a - 3)}^{2}$ as $(2 a - 3) (2 a - 3)$ .

$- 3 a^{2} + 15 a - 4 ((2 a - 3) (2 a - 3)) - a (a - 1)$

Step 1.6

Expand $(2 a - 3) (2 a - 3)$ using the FOIL Method.

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Step 1.6.1

Apply the distributive property.

$- 3 a^{2} + 15 a - 4 (2 a (2 a - 3) - 3 (2 a - 3)) - a (a - 1)$

Step 1.6.2

Apply the distributive property.

$- 3 a^{2} + 15 a - 4 (2 a (2 a) + 2 a \cdot - 3 - 3 (2 a - 3)) - a (a - 1)$

Step 1.6.3

Apply the distributive property.

$- 3 a^{2} + 15 a - 4 (2 a (2 a) + 2 a \cdot - 3 - 3 (2 a) - 3 \cdot - 3) - a (a - 1)$

Step 1.7

Simplify and combine like terms.

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Step 1.7.1

Simplify each term.

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Step 1.7.1.1

Rewrite using the commutative property of multiplication.

$- 3 a^{2} + 15 a - 4 (2 \cdot 2 a \cdot a + 2 a \cdot - 3 - 3 (2 a) - 3 \cdot - 3) - a (a - 1)$

Step 1.7.1.2

Multiply $a$ by $a$ by adding the exponents.

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Step 1.7.1.2.1

Move $a$ .

$- 3 a^{2} + 15 a - 4 (2 \cdot 2 (a \cdot a) + 2 a \cdot - 3 - 3 (2 a) - 3 \cdot - 3) - a (a - 1)$

Step 1.7.1.2.2

Multiply $a$ by $a$ .

$- 3 a^{2} + 15 a - 4 (2 \cdot 2 a^{2} + 2 a \cdot - 3 - 3 (2 a) - 3 \cdot - 3) - a (a - 1)$

Step 1.7.1.3

Multiply $2$ by $2$ .

$- 3 a^{2} + 15 a - 4 (4 a^{2} + 2 a \cdot - 3 - 3 (2 a) - 3 \cdot - 3) - a (a - 1)$

Step 1.7.1.4

Multiply $- 3$ by $2$ .

$- 3 a^{2} + 15 a - 4 (4 a^{2} - 6 a - 3 (2 a) - 3 \cdot - 3) - a (a - 1)$

Step 1.7.1.5

Multiply $2$ by $- 3$ .

$- 3 a^{2} + 15 a - 4 (4 a^{2} - 6 a - 6 a - 3 \cdot - 3) - a (a - 1)$

Step 1.7.1.6

Multiply $- 3$ by $- 3$ .

$- 3 a^{2} + 15 a - 4 (4 a^{2} - 6 a - 6 a + 9) - a (a - 1)$

Step 1.7.2

Subtract $6 a$ from $- 6 a$ .

$- 3 a^{2} + 15 a - 4 (4 a^{2} - 12 a + 9) - a (a - 1)$

Step 1.8

Apply the distributive property.

$- 3 a^{2} + 15 a - 4 (4 a^{2}) - 4 (- 12 a) - 4 \cdot 9 - a (a - 1)$

Step 1.9

Simplify.

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Step 1.9.1

Multiply $4$ by $- 4$ .

$- 3 a^{2} + 15 a - 16 a^{2} - 4 (- 12 a) - 4 \cdot 9 - a (a - 1)$

Step 1.9.2

Multiply $- 12$ by $- 4$ .

$- 3 a^{2} + 15 a - 16 a^{2} + 48 a - 4 \cdot 9 - a (a - 1)$

Step 1.9.3

Multiply $- 4$ by $9$ .

$- 3 a^{2} + 15 a - 16 a^{2} + 48 a - 36 - a (a - 1)$

Step 1.10

Apply the distributive property.

$- 3 a^{2} + 15 a - 16 a^{2} + 48 a - 36 - a \cdot a - a \cdot - 1$

Step 1.11

Multiply $a$ by $a$ by adding the exponents.

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Step 1.11.1

Move $a$ .

$- 3 a^{2} + 15 a - 16 a^{2} + 48 a - 36 - (a \cdot a) - a \cdot - 1$

Step 1.11.2

Multiply $a$ by $a$ .

$- 3 a^{2} + 15 a - 16 a^{2} + 48 a - 36 - a^{2} - a \cdot - 1$

Step 1.12

Multiply $- a \cdot - 1$ .

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Step 1.12.1

Multiply $- 1$ by $- 1$ .

$- 3 a^{2} + 15 a - 16 a^{2} + 48 a - 36 - a^{2} + 1 a$

Step 1.12.2

Multiply $a$ by $1$ .

$- 3 a^{2} + 15 a - 16 a^{2} + 48 a - 36 - a^{2} + a$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $16 a^{2}$ from $- 3 a^{2}$ .

$- 19 a^{2} + 15 a + 48 a - 36 - a^{2} + a$

Step 2.2

Subtract $a^{2}$ from $- 19 a^{2}$ .

$- 20 a^{2} + 15 a + 48 a - 36 + a$

Step 2.3

Add $15 a$ and $48 a$ .

$- 20 a^{2} + 63 a - 36 + a$

Step 2.4

Add $63 a$ and $a$ .

$- 20 a^{2} + 64 a - 36$