Simplify (a+b)(2a+3b)(2x-y)

$(a + b) (2 a + 3 b) (2 x - y)$

Step 1

Expand $(a + b) (2 a + 3 b)$ using the FOIL Method.

Apply the distributive property.

$(a (2 a + 3 b) + b (2 a + 3 b)) (2 x - y)$

Apply the distributive property.

$(a (2 a) + a (3 b) + b (2 a + 3 b)) (2 x - y)$

Apply the distributive property.

$(a (2 a) + a (3 b) + b (2 a) + b (3 b)) (2 x - y)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$(2 a \cdot a + a (3 b) + b (2 a) + b (3 b)) (2 x - y)$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$(2 (a \cdot a) + a (3 b) + b (2 a) + b (3 b)) (2 x - y)$

Multiply $a$ by $a$ .

$(2 a^{2} + a (3 b) + b (2 a) + b (3 b)) (2 x - y)$

Rewrite using the commutative property of multiplication.

$(2 a^{2} + 3 a b + b (2 a) + b (3 b)) (2 x - y)$

Rewrite using the commutative property of multiplication.

$(2 a^{2} + 3 a b + 2 b a + b (3 b)) (2 x - y)$

Rewrite using the commutative property of multiplication.

$(2 a^{2} + 3 a b + 2 b a + 3 b \cdot b) (2 x - y)$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$(2 a^{2} + 3 a b + 2 b a + 3 (b \cdot b)) (2 x - y)$

Multiply $b$ by $b$ .

$(2 a^{2} + 3 a b + 2 b a + 3 b^{2}) (2 x - y)$

Add $3 a b$ and $2 b a$ .

Move $b$ .

$(2 a^{2} + 3 a b + 2 a b + 3 b^{2}) (2 x - y)$

Add $3 a b$ and $2 a b$ .

$(2 a^{2} + 5 a b + 3 b^{2}) (2 x - y)$

Step 3

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

$2 a^{2} (2 x) + 2 a^{2} (- y) + 5 a b (2 x) + 5 a b (- y) + 3 b^{2} (2 x) + 3 b^{2} (- y)$

Step 4

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 a^{2} x + 2 a^{2} (- y) + 5 a b (2 x) + 5 a b (- y) + 3 b^{2} (2 x) + 3 b^{2} (- y)$

Multiply $2$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $2$ by $- 1$ .

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

Multiply $2$ by $5$ .

$4 a^{2} x - 2 a^{2} y + 10 a b x + 5 a b (- y) + 3 b^{2} (2 x) + 3 b^{2} (- y)$

Multiply $- 1$ by $5$ .

$4 a^{2} x - 2 a^{2} y + 10 a b x - 5 a b y + 3 b^{2} (2 x) + 3 b^{2} (- y)$

Rewrite using the commutative property of multiplication.

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

Multiply $3$ by $2$ .

$4 a^{2} x - 2 a^{2} y + 10 a b x - 5 a b y + 6 b^{2} x + 3 b^{2} (- y)$

Rewrite using the commutative property of multiplication.

$4 a^{2} x - 2 a^{2} y + 10 a b x - 5 a b y + 6 b^{2} x + 3 \cdot - 1 b^{2} y$

Multiply $3$ by $- 1$ .

$4 a^{2} x - 2 a^{2} y + 10 a b x - 5 a b y + 6 b^{2} x - 3 b^{2} y$

Simplify (a+b)(2a+3b)(2x-y)

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