Simplify (a-1)(2a+3)(4a-5)

$(a - 1) (2 a + 3) (4 a - 5)$

Step 1

Expand

$(a - 1) (2 a + 3)$ using the FOIL Method.

Apply the distributive property.

$(a (2 a + 3) - 1 (2 a + 3)) (4 a - 5)$

Apply the distributive property.

$(a (2 a) + a \cdot 3 - 1 (2 a + 3)) (4 a - 5)$

Apply the distributive property.

$(a (2 a) + a \cdot 3 - 1 (2 a) - 1 \cdot 3) (4 a - 5)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$(2 a \cdot a + a \cdot 3 - 1 (2 a) - 1 \cdot 3) (4 a - 5)$

Multiply

$a$ by

$a$ by adding the exponents.

Move

$a$ .

$(2 (a \cdot a) + a \cdot 3 - 1 (2 a) - 1 \cdot 3) (4 a - 5)$

Multiply

$a$ by

$a$ .

$(2 a^{2} + a \cdot 3 - 1 (2 a) - 1 \cdot 3) (4 a - 5)$

Move

$3$ to the left of

$a$ .

$(2 a^{2} + 3 \cdot a - 1 (2 a) - 1 \cdot 3) (4 a - 5)$

Multiply

$2$ by

$- 1$ .

$(2 a^{2} + 3 a - 2 a - 1 \cdot 3) (4 a - 5)$

Multiply

$- 1$ by

$3$ .

$(2 a^{2} + 3 a - 2 a - 3) (4 a - 5)$

Subtract

$2 a$ from

$3 a$ .

$(2 a^{2} + a - 3) (4 a - 5)$

Step 3

Expand

$(2 a^{2} + a - 3) (4 a - 5)$ by multiplying each term in the first expression by each term in the second expression.

$2 a^{2} (4 a) + 2 a^{2} \cdot - 5 + a (4 a) + a \cdot - 5 - 3 (4 a) - 3 \cdot - 5$

Step 4

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 4 a^{2} a + 2 a^{2} \cdot - 5 + a (4 a) + a \cdot - 5 - 3 (4 a) - 3 \cdot - 5$

Multiply

$a^{2}$ by

$a$ by adding the exponents.

Move

$a$ .

$2 \cdot 4 (a \cdot a^{2}) + 2 a^{2} \cdot - 5 + a (4 a) + a \cdot - 5 - 3 (4 a) - 3 \cdot - 5$

Multiply

$a$ by

$a^{2}$ .

Raise

$a$ to the power of

$1$ .

$2 \cdot 4 (a^{1} a^{2}) + 2 a^{2} \cdot - 5 + a (4 a) + a \cdot - 5 - 3 (4 a) - 3 \cdot - 5$

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 \cdot 4 a^{1 + 2} + 2 a^{2} \cdot - 5 + a (4 a) + a \cdot - 5 - 3 (4 a) - 3 \cdot - 5$

Add

$1$ and

$2$ .

$2 \cdot 4 a^{3} + 2 a^{2} \cdot - 5 + a (4 a) + a \cdot - 5 - 3 (4 a) - 3 \cdot - 5$

Multiply

$2$ by

$4$ .

$8 a^{3} + 2 a^{2} \cdot - 5 + a (4 a) + a \cdot - 5 - 3 (4 a) - 3 \cdot - 5$

Multiply

$- 5$ by

$2$ .

$8 a^{3} - 10 a^{2} + a (4 a) + a \cdot - 5 - 3 (4 a) - 3 \cdot - 5$

Rewrite using the commutative property of multiplication.

$8 a^{3} - 10 a^{2} + 4 a \cdot a + a \cdot - 5 - 3 (4 a) - 3 \cdot - 5$

Multiply

$a$ by

$a$ by adding the exponents.

Move

$a$ .

$8 a^{3} - 10 a^{2} + 4 (a \cdot a) + a \cdot - 5 - 3 (4 a) - 3 \cdot - 5$

Multiply

$a$ by

$a$ .

$8 a^{3} - 10 a^{2} + 4 a^{2} + a \cdot - 5 - 3 (4 a) - 3 \cdot - 5$

Move

$- 5$ to the left of

$a$ .

$8 a^{3} - 10 a^{2} + 4 a^{2} - 5 \cdot a - 3 (4 a) - 3 \cdot - 5$

Multiply

$4$ by

$- 3$ .

$8 a^{3} - 10 a^{2} + 4 a^{2} - 5 a - 12 a - 3 \cdot - 5$

Multiply

$- 3$ by

$- 5$ .

$8 a^{3} - 10 a^{2} + 4 a^{2} - 5 a - 12 a + 15$

Simplify by adding terms.

Add

$- 10 a^{2}$ and

$4 a^{2}$ .

$8 a^{3} - 6 a^{2} - 5 a - 12 a + 15$

Subtract

$12 a$ from

$- 5 a$ .

$8 a^{3} - 6 a^{2} - 17 a + 15$

Simplify (a-1)(2a+3)(4a-5)

Related Questions