Trigonometry Examples

$- {(4 h - 7)}^{2} - {(5 - 3 h)}^{2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(4 h - 7)}^{2}$ as $(4 h - 7) (4 h - 7)$ .

$- ((4 h - 7) (4 h - 7)) - {(5 - 3 h)}^{2}$

Step 1.2

Expand $(4 h - 7) (4 h - 7)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$- (4 h (4 h - 7) - 7 (4 h - 7)) - {(5 - 3 h)}^{2}$

Step 1.2.2

Apply the distributive property.

$- (4 h (4 h) + 4 h \cdot - 7 - 7 (4 h - 7)) - {(5 - 3 h)}^{2}$

Step 1.2.3

Apply the distributive property.

$- (4 h (4 h) + 4 h \cdot - 7 - 7 (4 h) - 7 \cdot - 7) - {(5 - 3 h)}^{2}$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Rewrite using the commutative property of multiplication.

$- (4 \cdot 4 h \cdot h + 4 h \cdot - 7 - 7 (4 h) - 7 \cdot - 7) - {(5 - 3 h)}^{2}$

Step 1.3.1.2

Multiply $h$ by $h$ by adding the exponents.

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Step 1.3.1.2.1

Move $h$ .

$- (4 \cdot 4 (h \cdot h) + 4 h \cdot - 7 - 7 (4 h) - 7 \cdot - 7) - {(5 - 3 h)}^{2}$

Step 1.3.1.2.2

Multiply $h$ by $h$ .

$- (4 \cdot 4 h^{2} + 4 h \cdot - 7 - 7 (4 h) - 7 \cdot - 7) - {(5 - 3 h)}^{2}$

Step 1.3.1.3

Multiply $4$ by $4$ .

$- (16 h^{2} + 4 h \cdot - 7 - 7 (4 h) - 7 \cdot - 7) - {(5 - 3 h)}^{2}$

Step 1.3.1.4

Multiply $- 7$ by $4$ .

$- (16 h^{2} - 28 h - 7 (4 h) - 7 \cdot - 7) - {(5 - 3 h)}^{2}$

Step 1.3.1.5

Multiply $4$ by $- 7$ .

$- (16 h^{2} - 28 h - 28 h - 7 \cdot - 7) - {(5 - 3 h)}^{2}$

Step 1.3.1.6

Multiply $- 7$ by $- 7$ .

$- (16 h^{2} - 28 h - 28 h + 49) - {(5 - 3 h)}^{2}$

Step 1.3.2

Subtract $28 h$ from $- 28 h$ .

$- (16 h^{2} - 56 h + 49) - {(5 - 3 h)}^{2}$

Step 1.4

Apply the distributive property.

$- (16 h^{2}) - (- 56 h) - 1 \cdot 49 - {(5 - 3 h)}^{2}$

Step 1.5

Simplify.

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Step 1.5.1

Multiply $16$ by $- 1$ .

$- 16 h^{2} - (- 56 h) - 1 \cdot 49 - {(5 - 3 h)}^{2}$

Step 1.5.2

Multiply $- 56$ by $- 1$ .

$- 16 h^{2} + 56 h - 1 \cdot 49 - {(5 - 3 h)}^{2}$

Step 1.5.3

Multiply $- 1$ by $49$ .

$- 16 h^{2} + 56 h - 49 - {(5 - 3 h)}^{2}$

Step 1.6

Rewrite ${(5 - 3 h)}^{2}$ as $(5 - 3 h) (5 - 3 h)$ .

$- 16 h^{2} + 56 h - 49 - ((5 - 3 h) (5 - 3 h))$

Step 1.7

Expand $(5 - 3 h) (5 - 3 h)$ using the FOIL Method.

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Step 1.7.1

Apply the distributive property.

$- 16 h^{2} + 56 h - 49 - (5 (5 - 3 h) - 3 h (5 - 3 h))$

Step 1.7.2

Apply the distributive property.

$- 16 h^{2} + 56 h - 49 - (5 \cdot 5 + 5 (- 3 h) - 3 h (5 - 3 h))$

Step 1.7.3

Apply the distributive property.

$- 16 h^{2} + 56 h - 49 - (5 \cdot 5 + 5 (- 3 h) - 3 h \cdot 5 - 3 h (- 3 h))$

Step 1.8

Simplify and combine like terms.

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Step 1.8.1

Simplify each term.

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Step 1.8.1.1

Multiply $5$ by $5$ .

$- 16 h^{2} + 56 h - 49 - (25 + 5 (- 3 h) - 3 h \cdot 5 - 3 h (- 3 h))$

Step 1.8.1.2

Multiply $- 3$ by $5$ .

$- 16 h^{2} + 56 h - 49 - (25 - 15 h - 3 h \cdot 5 - 3 h (- 3 h))$

Step 1.8.1.3

Multiply $5$ by $- 3$ .

$- 16 h^{2} + 56 h - 49 - (25 - 15 h - 15 h - 3 h (- 3 h))$

Step 1.8.1.4

Rewrite using the commutative property of multiplication.

$- 16 h^{2} + 56 h - 49 - (25 - 15 h - 15 h - 3 \cdot - 3 h \cdot h)$

Step 1.8.1.5

Multiply $h$ by $h$ by adding the exponents.

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Step 1.8.1.5.1

Move $h$ .

$- 16 h^{2} + 56 h - 49 - (25 - 15 h - 15 h - 3 \cdot - 3 (h \cdot h))$

Step 1.8.1.5.2

Multiply $h$ by $h$ .

$- 16 h^{2} + 56 h - 49 - (25 - 15 h - 15 h - 3 \cdot - 3 h^{2})$

Step 1.8.1.6

Multiply $- 3$ by $- 3$ .

$- 16 h^{2} + 56 h - 49 - (25 - 15 h - 15 h + 9 h^{2})$

Step 1.8.2

Subtract $15 h$ from $- 15 h$ .

$- 16 h^{2} + 56 h - 49 - (25 - 30 h + 9 h^{2})$

Step 1.9

Apply the distributive property.

$- 16 h^{2} + 56 h - 49 - 1 \cdot 25 - (- 30 h) - (9 h^{2})$

Step 1.10

Simplify.

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Step 1.10.1

Multiply $- 1$ by $25$ .

$- 16 h^{2} + 56 h - 49 - 25 - (- 30 h) - (9 h^{2})$

Step 1.10.2

Multiply $- 30$ by $- 1$ .

$- 16 h^{2} + 56 h - 49 - 25 + 30 h - (9 h^{2})$

Step 1.10.3

Multiply $9$ by $- 1$ .

$- 16 h^{2} + 56 h - 49 - 25 + 30 h - 9 h^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $9 h^{2}$ from $- 16 h^{2}$ .

$- 25 h^{2} + 56 h - 49 - 25 + 30 h$

Step 2.2

Add $56 h$ and $30 h$ .

$- 25 h^{2} + 86 h - 49 - 25$

Step 2.3

Subtract $25$ from $- 49$ .

$- 25 h^{2} + 86 h - 74$