Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Apply the distributive property.

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

Step 1.2.3

Apply the distributive property.

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

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.

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

Step 1.3.1.2

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

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Step 1.3.1.2.1

Move $x$ .

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

Step 1.3.1.2.2

Multiply $x$ by $x$ .

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

Step 1.3.1.3

Multiply $3$ by $3$ .

$9 x^{2} + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2 + {(4 x + 5)}^{2}$

Step 1.3.1.4

Multiply $- 2$ by $3$ .

$9 x^{2} - 6 x - 2 (3 x) - 2 \cdot - 2 + {(4 x + 5)}^{2}$

Step 1.3.1.5

Multiply $3$ by $- 2$ .

$9 x^{2} - 6 x - 6 x - 2 \cdot - 2 + {(4 x + 5)}^{2}$

Step 1.3.1.6

Multiply $- 2$ by $- 2$ .

$9 x^{2} - 6 x - 6 x + 4 + {(4 x + 5)}^{2}$

Step 1.3.2

Subtract $6 x$ from $- 6 x$ .

$9 x^{2} - 12 x + 4 + {(4 x + 5)}^{2}$

Step 1.4

Rewrite ${(4 x + 5)}^{2}$ as $(4 x + 5) (4 x + 5)$ .

$9 x^{2} - 12 x + 4 + (4 x + 5) (4 x + 5)$

Step 1.5

Expand $(4 x + 5) (4 x + 5)$ using the FOIL Method.

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Step 1.5.1

Apply the distributive property.

$9 x^{2} - 12 x + 4 + 4 x (4 x + 5) + 5 (4 x + 5)$

Step 1.5.2

Apply the distributive property.

$9 x^{2} - 12 x + 4 + 4 x (4 x) + 4 x \cdot 5 + 5 (4 x + 5)$

Step 1.5.3

Apply the distributive property.

$9 x^{2} - 12 x + 4 + 4 x (4 x) + 4 x \cdot 5 + 5 (4 x) + 5 \cdot 5$

Step 1.6

Simplify and combine like terms.

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Step 1.6.1

Simplify each term.

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Step 1.6.1.1

Rewrite using the commutative property of multiplication.

$9 x^{2} - 12 x + 4 + 4 \cdot 4 x \cdot x + 4 x \cdot 5 + 5 (4 x) + 5 \cdot 5$

Step 1.6.1.2

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

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Step 1.6.1.2.1

Move $x$ .

$9 x^{2} - 12 x + 4 + 4 \cdot 4 (x \cdot x) + 4 x \cdot 5 + 5 (4 x) + 5 \cdot 5$

Step 1.6.1.2.2

Multiply $x$ by $x$ .

$9 x^{2} - 12 x + 4 + 4 \cdot 4 x^{2} + 4 x \cdot 5 + 5 (4 x) + 5 \cdot 5$

Step 1.6.1.3

Multiply $4$ by $4$ .

$9 x^{2} - 12 x + 4 + 16 x^{2} + 4 x \cdot 5 + 5 (4 x) + 5 \cdot 5$

Step 1.6.1.4

Multiply $5$ by $4$ .

$9 x^{2} - 12 x + 4 + 16 x^{2} + 20 x + 5 (4 x) + 5 \cdot 5$

Step 1.6.1.5

Multiply $4$ by $5$ .

$9 x^{2} - 12 x + 4 + 16 x^{2} + 20 x + 20 x + 5 \cdot 5$

Step 1.6.1.6

Multiply $5$ by $5$ .

$9 x^{2} - 12 x + 4 + 16 x^{2} + 20 x + 20 x + 25$

Step 1.6.2

Add $20 x$ and $20 x$ .

$9 x^{2} - 12 x + 4 + 16 x^{2} + 40 x + 25$

Step 2

Simplify by adding terms.

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Step 2.1

Add $9 x^{2}$ and $16 x^{2}$ .

$25 x^{2} - 12 x + 4 + 40 x + 25$

Step 2.2

Add $- 12 x$ and $40 x$ .

$25 x^{2} + 28 x + 4 + 25$

Step 2.3

Add $4$ and $25$ .

$25 x^{2} + 28 x + 29$