Algebra Examples

$8 p (p + 6) - 7 p (3 - 8 p)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$8 p \cdot p + 8 p \cdot 6 - 7 p (3 - 8 p)$

Step 1.2

Multiply $p$ by $p$ by adding the exponents.

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Step 1.2.1

Move $p$ .

$8 (p \cdot p) + 8 p \cdot 6 - 7 p (3 - 8 p)$

Step 1.2.2

Multiply $p$ by $p$ .

$8 p^{2} + 8 p \cdot 6 - 7 p (3 - 8 p)$

$8 p^{2} + 8 p \cdot 6 - 7 p (3 - 8 p)$

Step 1.3

Multiply $6$ by $8$ .

$8 p^{2} + 48 p - 7 p (3 - 8 p)$

Step 1.4

Apply the distributive property.

$8 p^{2} + 48 p - 7 p \cdot 3 - 7 p (- 8 p)$

Step 1.5

Multiply $3$ by $- 7$ .

$8 p^{2} + 48 p - 21 p - 7 p (- 8 p)$

Step 1.6

Rewrite using the commutative property of multiplication.

$8 p^{2} + 48 p - 21 p - 7 \cdot - 8 p \cdot p$

Step 1.7

Simplify each term.

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Step 1.7.1

Multiply $p$ by $p$ by adding the exponents.

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Step 1.7.1.1

Move $p$ .

$8 p^{2} + 48 p - 21 p - 7 \cdot - 8 (p \cdot p)$

Step 1.7.1.2

Multiply $p$ by $p$ .

$8 p^{2} + 48 p - 21 p - 7 \cdot - 8 p^{2}$

$8 p^{2} + 48 p - 21 p - 7 \cdot - 8 p^{2}$

Step 1.7.2

Multiply $- 7$ by $- 8$ .

$8 p^{2} + 48 p - 21 p + 56 p^{2}$

$8 p^{2} + 48 p - 21 p + 56 p^{2}$

$8 p^{2} + 48 p - 21 p + 56 p^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $8 p^{2}$ and $56 p^{2}$ .

$64 p^{2} + 48 p - 21 p$

Step 2.2

Subtract $21 p$ from $48 p$ .

$64 p^{2} + 27 p$

$64 p^{2} + 27 p$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$