Algebra Examples

$8 y^{2} - 5 y + 7$ from $2 y^{2} + 7 y + 11$

Step 1

Write the problem as a mathematical expression.

$2 y^{2} + 7 y + 11 - (8 y^{2} - 5 y + 7)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$2 y^{2} + 7 y + 11 - (8 y^{2}) - (- 5 y) - 1 \cdot 7$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $8$ by $- 1$ .

$2 y^{2} + 7 y + 11 - 8 y^{2} - (- 5 y) - 1 \cdot 7$

Step 2.2.2

Multiply $- 5$ by $- 1$ .

$2 y^{2} + 7 y + 11 - 8 y^{2} + 5 y - 1 \cdot 7$

Step 2.2.3

Multiply $- 1$ by $7$ .

$2 y^{2} + 7 y + 11 - 8 y^{2} + 5 y - 7$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $8 y^{2}$ from $2 y^{2}$ .

$- 6 y^{2} + 7 y + 11 + 5 y - 7$

Step 3.2

Add $7 y$ and $5 y$ .

$- 6 y^{2} + 12 y + 11 - 7$

Step 3.3

Subtract $7$ from $11$ .

$- 6 y^{2} + 12 y + 4$