Solve (13-5a)^2-24(-6a^2-13a^5)

Question

Simplify the expression

169 - 130 a + 169 a^{2} + 312 a^{5}

Evaluate

(13 - 5 a)^{2} - 24 (- 6 a^{2} - 13 a^{5})

Expand the expression

169 - 130 a + 25 a^{2} - 24 (- 6 a^{2} - 13 a^{5})

Expand the expression

More Steps

Calculate

- 24 (- 6 a^{2} - 13 a^{5})

Apply the distributive property

- 24 (- 6 a^{2}) - (- 24 \times 13 a^{5})

Multiply the numbers

More Steps

Evaluate

- 24 (- 6)

Multiplying or dividing an even number of negative terms equals a positive

24 \times 6

Multiply the numbers

144

144 a^{2} - (- 24 \times 13 a^{5})

Multiply the numbers

144 a^{2} - (- 312 a^{5})

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

144 a^{2} + 312 a^{5}

169 - 130 a + 25 a^{2} + 144 a^{2} + 312 a^{5}

Solution

More Steps

Evaluate

25 a^{2} + 144 a^{2}

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

(25 + 144) a^{2}

Add the numbers

169 a^{2}

169 - 130 a + 169 a^{2} + 312 a^{5}

Show Solution

Factor the expression

13 (13 - 10 a + 13 a^{2} + 24 a^{5})

Evaluate

(13 - 5 a)^{2} - 24 (- 6 a^{2} - 13 a^{5})

Simplify

More Steps

Evaluate

(13 - 5 a)^{2}

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

1 3^{2} - 2 \times 13 \times 5 a + (5 a)^{2}

Calculate

169 - 130 a + 25 a^{2}

169 - 130 a + 25 a^{2} - 24 (- 6 a^{2} - 13 a^{5})

Simplify

More Steps

Evaluate

- 24 (- 6 a^{2} - 13 a^{5})

Apply the distributive property

- 24 (- 6 a^{2}) - 24 (- 13 a^{5})

Multiply the terms

More Steps

Evaluate

- 24 (- 6)

Multiplying or dividing an even number of negative terms equals a positive

24 \times 6

Multiply the numbers

144

144 a^{2} - 24 (- 13 a^{5})

Multiply the terms

More Steps

Evaluate

- 24 (- 13)

Multiplying or dividing an even number of negative terms equals a positive

24 \times 13

Multiply the numbers

312

144 a^{2} + 312 a^{5}

169 - 130 a + 25 a^{2} + 144 a^{2} + 312 a^{5}

Add the terms

More Steps

Evaluate

25 a^{2} + 144 a^{2}

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

(25 + 144) a^{2}

Add the numbers

169 a^{2}

169 - 130 a + 169 a^{2} + 312 a^{5}

Solution

13 (13 - 10 a + 13 a^{2} + 24 a^{5})

Show Solution