Basic Math Examples

$18 a^{2} + 8 a^{2} y - 45 a - 20 a y + 28 a + 63$

Step 1

Regroup terms.

$- 45 a + 63 + 18 a^{2} + 8 a^{2} y - 20 a y + 28 a$

Step 2

Factor $- 9$ out of $- 45 a + 63$ .

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Step 2.1

Factor $- 9$ out of $- 45 a$ .

$- 9 (5 a) + 63 + 18 a^{2} + 8 a^{2} y - 20 a y + 28 a$

Step 2.2

Factor $- 9$ out of $63$ .

$- 9 (5 a) - 9 (- 7) + 18 a^{2} + 8 a^{2} y - 20 a y + 28 a$

Step 2.3

Factor $- 9$ out of $- 9 (5 a) - 9 (- 7)$ .

$- 9 (5 a - 7) + 18 a^{2} + 8 a^{2} y - 20 a y + 28 a$

Step 3

Factor $2 a$ out of $18 a^{2} + 8 a^{2} y - 20 a y + 28 a$ .

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Step 3.1

Factor $2 a$ out of $18 a^{2}$ .

$- 9 (5 a - 7) + 2 a (9 a) + 8 a^{2} y - 20 a y + 28 a$

Step 3.2

Factor $2 a$ out of $8 a^{2} y$ .

$- 9 (5 a - 7) + 2 a (9 a) + 2 a (4 a y) - 20 a y + 28 a$

Step 3.3

Factor $2 a$ out of $- 20 a y$ .

$- 9 (5 a - 7) + 2 a (9 a) + 2 a (4 a y) + 2 a (- 10 y) + 28 a$

Step 3.4

Factor $2 a$ out of $28 a$ .

$- 9 (5 a - 7) + 2 a (9 a) + 2 a (4 a y) + 2 a (- 10 y) + 2 a (14)$

Step 3.5

Factor $2 a$ out of $2 a (9 a) + 2 a (4 a y)$ .

$- 9 (5 a - 7) + 2 a (9 a + 4 a y) + 2 a (- 10 y) + 2 a (14)$

Step 3.6

Factor $2 a$ out of $2 a (9 a + 4 a y) + 2 a (- 10 y)$ .

$- 9 (5 a - 7) + 2 a (9 a + 4 a y - 10 y) + 2 a (14)$

Step 3.7

Factor $2 a$ out of $2 a (9 a + 4 a y - 10 y) + 2 a (14)$ .

$- 9 (5 a - 7) + 2 a (9 a + 4 a y - 10 y + 14)$

Step 4

Factor $- 1$ out of $- 9 (5 a - 7) + 2 a (9 a + 4 a y - 10 y + 14)$ .

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Step 4.1

Reorder the expression.

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Step 4.1.1

Reorder $9 a$ and $4 a y$ .

$- 9 (5 a - 7) + 2 a (4 a y + 9 a - 10 y + 14)$

Step 4.1.2

Reorder $- 9 (5 a - 7)$ and $2 a (4 a y + 9 a - 10 y + 14)$ .

$2 a (4 a y + 9 a - 10 y + 14) - 9 (5 a - 7)$

Step 4.2

Factor $- 1$ out of $2 a (4 a y + 9 a - 10 y + 14)$ .

$- (- 2 a (4 a y + 9 a - 10 y + 14)) - 9 (5 a - 7)$

Step 4.3

Factor $- 1$ out of $- 9 (5 a - 7)$ .

$- (- 2 a (4 a y + 9 a - 10 y + 14)) - (9 (5 a - 7))$

Step 4.4

Factor $- 1$ out of $- (- 2 a (4 a y + 9 a - 10 y + 14)) - (9 (5 a - 7))$ .

$- (- 2 a (4 a y + 9 a - 10 y + 14) + 9 (5 a - 7))$

Step 5

Apply the distributive property.

$- (- 2 a (4 a y) - 2 a (9 a) - 2 a (- 10 y) - 2 a \cdot 14 + 9 (5 a - 7))$

Step 6

Simplify.

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Step 6.1

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

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Step 6.1.1

Move $a$ .

$- (- 2 (a \cdot a) (4 y) - 2 a (9 a) - 2 a (- 10 y) - 2 a \cdot 14 + 9 (5 a - 7))$

Step 6.1.2

Multiply $a$ by $a$ .

$- (- 2 a^{2} (4 y) - 2 a (9 a) - 2 a (- 10 y) - 2 a \cdot 14 + 9 (5 a - 7))$

Step 6.2

Rewrite using the commutative property of multiplication.

$- (- 2 a^{2} (4 y) - 2 \cdot 9 a \cdot a - 2 a (- 10 y) - 2 a \cdot 14 + 9 (5 a - 7))$

Step 6.3

Rewrite using the commutative property of multiplication.

$- (- 2 a^{2} (4 y) - 2 \cdot 9 a \cdot a - 2 \cdot - 10 a y - 2 a \cdot 14 + 9 (5 a - 7))$

Step 6.4

Multiply $14$ by $- 2$ .

$- (- 2 a^{2} (4 y) - 2 \cdot 9 a \cdot a - 2 \cdot - 10 a y - 28 a + 9 (5 a - 7))$

Step 7

Simplify each term.

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Step 7.1

Rewrite using the commutative property of multiplication.

$- (- 2 \cdot 4 a^{2} y - 2 \cdot 9 a \cdot a - 2 \cdot - 10 a y - 28 a + 9 (5 a - 7))$

Step 7.2

Multiply $- 2$ by $4$ .

$- (- 8 a^{2} y - 2 \cdot 9 a \cdot a - 2 \cdot - 10 a y - 28 a + 9 (5 a - 7))$

Step 7.3

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

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Step 7.3.1

Move $a$ .

$- (- 8 a^{2} y - 2 \cdot 9 (a \cdot a) - 2 \cdot - 10 a y - 28 a + 9 (5 a - 7))$

Step 7.3.2

Multiply $a$ by $a$ .

$- (- 8 a^{2} y - 2 \cdot 9 a^{2} - 2 \cdot - 10 a y - 28 a + 9 (5 a - 7))$

Step 7.4

Multiply $- 2$ by $9$ .

$- (- 8 a^{2} y - 18 a^{2} - 2 \cdot - 10 a y - 28 a + 9 (5 a - 7))$

Step 7.5

Multiply $- 2$ by $- 10$ .

$- (- 8 a^{2} y - 18 a^{2} + 20 a y - 28 a + 9 (5 a - 7))$

Step 8

Apply the distributive property.

$- (- 8 a^{2} y - 18 a^{2} + 20 a y - 28 a + 9 (5 a) + 9 \cdot - 7)$

Step 9

Multiply $5$ by $9$ .

$- (- 8 a^{2} y - 18 a^{2} + 20 a y - 28 a + 45 a + 9 \cdot - 7)$

Step 10

Multiply $9$ by $- 7$ .

$- (- 8 a^{2} y - 18 a^{2} + 20 a y - 28 a + 45 a - 63)$

Step 11

Add $- 28 a$ and $45 a$ .

$- (- 8 a^{2} y - 18 a^{2} + 20 a y + 17 a - 63)$