Simplify ( square root of 2a-5)(7 square root of 2a-5)

$(\sqrt{2 a} - 5) (7 \sqrt{2 a} - 5)$

Step 1

Expand $(\sqrt{2 a} - 5) (7 \sqrt{2 a} - 5)$ using the FOIL Method.

Apply the distributive property.

$\sqrt{2 a} (7 \sqrt{2 a} - 5) - 5 (7 \sqrt{2 a} - 5)$

Apply the distributive property.

$\sqrt{2 a} (7 \sqrt{2 a}) + \sqrt{2 a} \cdot - 5 - 5 (7 \sqrt{2 a} - 5)$

Apply the distributive property.

$\sqrt{2 a} (7 \sqrt{2 a}) + \sqrt{2 a} \cdot - 5 - 5 (7 \sqrt{2 a}) - 5 \cdot - 5$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$7 \sqrt{2 a} \sqrt{2 a} + \sqrt{2 a} \cdot - 5 - 5 (7 \sqrt{2 a}) - 5 \cdot - 5$

Multiply $7 \sqrt{2 a} \sqrt{2 a}$ .

Raise $\sqrt{2 a}$ to the power of $1$ .

$7 ({\sqrt{2 a}}^{1} \sqrt{2 a}) + \sqrt{2 a} \cdot - 5 - 5 (7 \sqrt{2 a}) - 5 \cdot - 5$

Raise $\sqrt{2 a}$ to the power of $1$ .

$7 ({\sqrt{2 a}}^{1} {\sqrt{2 a}}^{1}) + \sqrt{2 a} \cdot - 5 - 5 (7 \sqrt{2 a}) - 5 \cdot - 5$

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

$7 {\sqrt{2 a}}^{1 + 1} + \sqrt{2 a} \cdot - 5 - 5 (7 \sqrt{2 a}) - 5 \cdot - 5$

Add $1$ and $1$ .

$7 {\sqrt{2 a}}^{2} + \sqrt{2 a} \cdot - 5 - 5 (7 \sqrt{2 a}) - 5 \cdot - 5$

Rewrite ${\sqrt{2 a}}^{2}$ as $2 a$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 a}$ as ${(2 a)}^{\frac{1}{2}}$ .

$7 {({(2 a)}^{\frac{1}{2}})}^{2} + \sqrt{2 a} \cdot - 5 - 5 (7 \sqrt{2 a}) - 5 \cdot - 5$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$7 {(2 a)}^{\frac{1}{2} \cdot 2} + \sqrt{2 a} \cdot - 5 - 5 (7 \sqrt{2 a}) - 5 \cdot - 5$

Combine $\frac{1}{2}$ and $2$ .

$7 {(2 a)}^{\frac{2}{2}} + \sqrt{2 a} \cdot - 5 - 5 (7 \sqrt{2 a}) - 5 \cdot - 5$

Cancel the common factor of $2$ .

Cancel the common factor.

$7 {(2 a)}^{\frac{2}{2}} + \sqrt{2 a} \cdot - 5 - 5 (7 \sqrt{2 a}) - 5 \cdot - 5$

Rewrite the expression.

$7 {(2 a)}^{1} + \sqrt{2 a} \cdot - 5 - 5 (7 \sqrt{2 a}) - 5 \cdot - 5$

Simplify.

$7 (2 a) + \sqrt{2 a} \cdot - 5 - 5 (7 \sqrt{2 a}) - 5 \cdot - 5$

Multiply $2$ by $7$ .

$14 a + \sqrt{2 a} \cdot - 5 - 5 (7 \sqrt{2 a}) - 5 \cdot - 5$

Move $- 5$ to the left of $\sqrt{2 a}$ .

$14 a - 5 \cdot \sqrt{2 a} - 5 (7 \sqrt{2 a}) - 5 \cdot - 5$

Multiply $7$ by $- 5$ .

$14 a - 5 \sqrt{2 a} - 35 \sqrt{2 a} - 5 \cdot - 5$

Multiply $- 5$ by $- 5$ .

$14 a - 5 \sqrt{2 a} - 35 \sqrt{2 a} + 25$

Subtract $35 \sqrt{2 a}$ from $- 5 \sqrt{2 a}$ .

$14 a - 40 \sqrt{2 a} + 25$

Simplify ( square root of 2a-5)(7 square root of 2a-5)

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