Basic Math Examples

${(41 - 17 h)}^{2} + {(16 h)}^{2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(41 - 17 h)}^{2}$ as $(41 - 17 h) (41 - 17 h)$ .

$(41 - 17 h) (41 - 17 h) + {(16 h)}^{2}$

Step 1.2

Expand $(41 - 17 h) (41 - 17 h)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$41 (41 - 17 h) - 17 h (41 - 17 h) + {(16 h)}^{2}$

Step 1.2.2

Apply the distributive property.

$41 \cdot 41 + 41 (- 17 h) - 17 h (41 - 17 h) + {(16 h)}^{2}$

Step 1.2.3

Apply the distributive property.

$41 \cdot 41 + 41 (- 17 h) - 17 h \cdot 41 - 17 h (- 17 h) + {(16 h)}^{2}$

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

Multiply $41$ by $41$ .

$1681 + 41 (- 17 h) - 17 h \cdot 41 - 17 h (- 17 h) + {(16 h)}^{2}$

Step 1.3.1.2

Multiply $- 17$ by $41$ .

$1681 - 697 h - 17 h \cdot 41 - 17 h (- 17 h) + {(16 h)}^{2}$

Step 1.3.1.3

Multiply $41$ by $- 17$ .

$1681 - 697 h - 697 h - 17 h (- 17 h) + {(16 h)}^{2}$

Step 1.3.1.4

Rewrite using the commutative property of multiplication.

$1681 - 697 h - 697 h - 17 \cdot - 17 h \cdot h + {(16 h)}^{2}$

Step 1.3.1.5

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

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Step 1.3.1.5.1

Move $h$ .

$1681 - 697 h - 697 h - 17 \cdot - 17 (h \cdot h) + {(16 h)}^{2}$

Step 1.3.1.5.2

Multiply $h$ by $h$ .

$1681 - 697 h - 697 h - 17 \cdot - 17 h^{2} + {(16 h)}^{2}$

Step 1.3.1.6

Multiply $- 17$ by $- 17$ .

$1681 - 697 h - 697 h + 289 h^{2} + {(16 h)}^{2}$

Step 1.3.2

Subtract $697 h$ from $- 697 h$ .

$1681 - 1394 h + 289 h^{2} + {(16 h)}^{2}$

Step 1.4

Apply the product rule to $16 h$ .

$1681 - 1394 h + 289 h^{2} + 16^{2} h^{2}$

Step 1.5

Raise $16$ to the power of $2$ .

$1681 - 1394 h + 289 h^{2} + 256 h^{2}$

Step 2

Add $289 h^{2}$ and $256 h^{2}$ .

$1681 - 1394 h + 545 h^{2}$