Solve (49-x^2)(25-x^2)

Question

Simplify the expression

1225 - 74 x^{2} + x^{4}

Evaluate

(49 - x^{2}) (25 - x^{2})

Apply the distributive property

49 \times 25 - 49 x^{2} - x^{2} \times 25 - (- x^{2} \times x^{2})

Multiply the numbers

1225 - 49 x^{2} - x^{2} \times 25 - (- x^{2} \times x^{2})

Use the commutative property to reorder the terms

1225 - 49 x^{2} - 25 x^{2} - (- x^{2} \times x^{2})

Multiply the terms

More Steps

Evaluate

x^{2} \times x^{2}

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

x^{2 + 2}

Add the numbers

x^{4}

1225 - 49 x^{2} - 25 x^{2} - (- x^{4})

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

1225 - 49 x^{2} - 25 x^{2} + x^{4}

Solution

More Steps

Evaluate

- 49 x^{2} - 25 x^{2}

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

(- 49 - 25) x^{2}

Subtract the numbers

- 74 x^{2}

1225 - 74 x^{2} + x^{4}

Show Solution

Factor the expression

(7 - x) (7 + x) (5 - x) (5 + x)

Evaluate

(49 - x^{2}) (25 - x^{2})

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(7 - x) (7 + x) (25 - x^{2})

Solution

(7 - x) (7 + x) (5 - x) (5 + x)

Show Solution

Find the roots

x_{1} = - 7, x_{2} = - 5, x_{3} = 5, x_{4} = 7

Evaluate

(49 - x^{2}) (25 - x^{2})

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

(49 - x^{2}) (25 - x^{2}) = 0

Separate the equation into 2 possible cases

49 - x^{2} = 0 25 - x^{2} = 0

Solve the equation

More Steps

Evaluate

49 - x^{2} = 0

Move the constant to the right-hand side and change its sign

- x^{2} = 0 - 49

Removing 0 doesn't change the value,so remove it from the expression

- x^{2} = - 49

Change the signs on both sides of the equation

x^{2} = 49

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 49

Simplify the expression

More Steps

Evaluate

49

Write the number in exponential form with the base of 7

7^{2}

Reduce the index of the radical and exponent with 2

7

x = \pm 7

Separate the equation into 2 possible cases

x = 7 x = - 7

x = 7 x = - 7 25 - x^{2} = 0

Solve the equation

More Steps

Evaluate

25 - x^{2} = 0

Move the constant to the right-hand side and change its sign

- x^{2} = 0 - 25

Removing 0 doesn't change the value,so remove it from the expression

- x^{2} = - 25

Change the signs on both sides of the equation

x^{2} = 25

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 25

Simplify the expression

More Steps

Evaluate

25

Write the number in exponential form with the base of 5

5^{2}

Reduce the index of the radical and exponent with 2

5

x = \pm 5

Separate the equation into 2 possible cases

x = 5 x = - 5

x = 7 x = - 7 x = 5 x = - 5

Solution

x_{1} = - 7, x_{2} = - 5, x_{3} = 5, x_{4} = 7

Show Solution