Algebra Examples

sum of $4 x^{3} \cdot 2 x^{2} - 4 x + 3$ and $7 x^{3} - 4 x^{2} + 7 x + 8$

Step 1

Write the problem as a mathematical expression.

$4 x^{3} \cdot 2 x^{2} - 4 x + 3 + 7 x^{3} - 4 x^{2} + 7 x + 8$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$4 \cdot 2 x^{3} x^{2} - 4 x + 3 + 7 x^{3} - 4 x^{2} + 7 x + 8$

Step 2.2

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

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Step 2.2.1

Move $x^{2}$ .

$4 \cdot 2 (x^{2} x^{3}) - 4 x + 3 + 7 x^{3} - 4 x^{2} + 7 x + 8$

Step 2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 \cdot 2 x^{2 + 3} - 4 x + 3 + 7 x^{3} - 4 x^{2} + 7 x + 8$

Step 2.2.3

Add $2$ and $3$ .

$4 \cdot 2 x^{5} - 4 x + 3 + 7 x^{3} - 4 x^{2} + 7 x + 8$

Step 2.3

Multiply $4$ by $2$ .

$8 x^{5} - 4 x + 3 + 7 x^{3} - 4 x^{2} + 7 x + 8$

Step 3

Simplify by adding terms.

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Step 3.1

Add $- 4 x$ and $7 x$ .

$8 x^{5} + 3 + 7 x^{3} - 4 x^{2} + 3 x + 8$

Step 3.2

Add $3$ and $8$ .

$8 x^{5} + 7 x^{3} - 4 x^{2} + 3 x + 11$