Solve (a^2 -7)(a^2)-(2a-1)(a-14)

Question

Simplify the expression

Solution

a^{4} - 9 a^{2} + 29 a - 14

Evaluate

(a^{2} - 7) a^{2} - (2 a - 1) (a - 14)

Multiply the terms

a^{2} (a^{2} - 7) - (2 a - 1) (a - 14)

Rewrite the expression

a^{2} (a^{2} - 7) + (- 2 a + 1) (a - 14)

Expand the expression

More Steps

Calculate

a^{2} (a^{2} - 7)

Apply the distributive property

a^{2} \times a^{2} - a^{2} \times 7

Multiply the terms

More Steps

Evaluate

a^{2} \times a^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

a^{2 + 2}

Add the numbers

a^{4}

a^{4} - a^{2} \times 7

Use the commutative property to reorder the terms

a^{4} - 7 a^{2}

a^{4} - 7 a^{2} + (- 2 a + 1) (a - 14)

Expand the expression

More Steps

Calculate

(- 2 a + 1) (a - 14)

Apply the distributive property

- 2 a \times a - (- 2 a \times 14) + 1 \times a - 1 \times 14

Multiply the terms

- 2 a^{2} - (- 2 a \times 14) + 1 \times a - 1 \times 14

Multiply the numbers

- 2 a^{2} - (- 28 a) + 1 \times a - 1 \times 14

Any expression multiplied by 1 remains the same

- 2 a^{2} - (- 28 a) + a - 1 \times 14

Any expression multiplied by 1 remains the same

- 2 a^{2} - (- 28 a) + a - 14

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 2 a^{2} + 28 a + a - 14

Add the terms

More Steps

Evaluate

28 a + a

Collect like terms by calculating the sum or difference of their coefficients

(28 + 1) a

Add the numbers

29 a

- 2 a^{2} + 29 a - 14

a^{4} - 7 a^{2} - 2 a^{2} + 29 a - 14

Solution

More Steps

Evaluate

- 7 a^{2} - 2 a^{2}

Collect like terms by calculating the sum or difference of their coefficients

(- 7 - 2) a^{2}

Subtract the numbers

- 9 a^{2}

a^{4} - 9 a^{2} + 29 a - 14

Show Solution

Find the roots

Find the roots of the algebra expression

a_{1} \approx - 4.109289, a_{2} \approx 0.584891

Evaluate

(a^{2} - 7) (a^{2}) - (2 a - 1) (a - 14)

To find the roots of the expression,set the expression equal to 0

(a^{2} - 7) (a^{2}) - (2 a - 1) (a - 14) = 0

Calculate

(a^{2} - 7) a^{2} - (2 a - 1) (a - 14) = 0

Multiply the terms

a^{2} (a^{2} - 7) - (2 a - 1) (a - 14) = 0

Rewrite the expression

a^{2} (a^{2} - 7) + (- 2 a + 1) (a - 14) = 0

Calculate

More Steps

Evaluate

a^{2} (a^{2} - 7) + (- 2 a + 1) (a - 14)

Expand the expression

More Steps

Calculate

a^{2} (a^{2} - 7)

Apply the distributive property

a^{2} \times a^{2} - a^{2} \times 7

Multiply the terms

a^{4} - a^{2} \times 7

Use the commutative property to reorder the terms

a^{4} - 7 a^{2}

a^{4} - 7 a^{2} + (- 2 a + 1) (a - 14)

Expand the expression

More Steps

Calculate

(- 2 a + 1) (a - 14)

Apply the distributive property

- 2 a \times a - (- 2 a \times 14) + 1 \times a - 1 \times 14

Multiply the terms

- 2 a^{2} - (- 2 a \times 14) + 1 \times a - 1 \times 14

Multiply the numbers

- 2 a^{2} - (- 28 a) + 1 \times a - 1 \times 14

Any expression multiplied by 1 remains the same

- 2 a^{2} - (- 28 a) + a - 1 \times 14

Any expression multiplied by 1 remains the same

- 2 a^{2} - (- 28 a) + a - 14

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 2 a^{2} + 28 a + a - 14

Add the terms

- 2 a^{2} + 29 a - 14

a^{4} - 7 a^{2} - 2 a^{2} + 29 a - 14

Subtract the terms

More Steps

Evaluate

- 7 a^{2} - 2 a^{2}

Collect like terms by calculating the sum or difference of their coefficients

(- 7 - 2) a^{2}

Subtract the numbers

- 9 a^{2}

a^{4} - 9 a^{2} + 29 a - 14

a^{4} - 9 a^{2} + 29 a - 14 = 0

Calculate

a \approx 0.584891 a \approx - 4.109289

Solution

a_{1} \approx - 4.109289, a_{2} \approx 0.584891

Show Solution

(a^2 7)(a^2) (2a 1)(a 14)

Simplify the expression

Solution

Find the roots

Find the roots of the algebra expression