(2x+7)(15y-5) (3x-7)
To expand the expression (2x+7)(15y-5)(3x-7), we can use the distributive property.
First, we expand (2x+7)(15y-5):
(2x+7)(15y-5) = 2x(15y-5) + 7(15y-5)
= 30xy - 10x + 105y - 35
Now, we can multiply this result by (3x-7):
(30xy - 10x + 105y - 35)(3x-7) = 30xy(3x-7) - 10x(3x-7) + 105y(3x-7) - 35(3x-7)
= 90x^2y - 210xy - 30x^2 + 70x + 315xy - 735y - 105x + 245 - 105x + 245
Combining like terms, we get:
= 90x^2y + 315xy - 30x^2 - 420x - 735y + 490
To simplify the expression (2x+7)(15y-5)(3x-7), you need to follow these steps:
Step 1: Distribute the first two terms (2x+7) into (15y-5):
(2x+7)(15y-5) = 2x(15y-5) + 7(15y-5)
Step 2: Simplify the expressions after distributing:
2x(15y-5) + 7(15y-5) = 30xy - 10x + 105y - 35
Step 3: Distribute the result from step 2 into the last term (3x-7):
(30xy - 10x + 105y - 35)(3x-7) = (30xy - 10x + 105y - 35)(3x) + (30xy - 10x + 105y - 35)(-7)
Step 4: Simplify the expressions after distributing:
(30xy - 10x + 105y - 35)(3x) = 90x^2y - 30x^2 + 315xy - 105x
(30xy - 10x + 105y - 35)(-7) = -210xy + 70x - 735y + 245
Step 5: Combine like terms:
90x^2y - 30x^2 + 315xy - 105x - 210xy + 70x - 735y + 245
= 90x^2y - 30x^2 + 105xy - 35x -735y + 245
So, the simplified expression is 90x^2y - 30x^2 + 105xy - 35x -735y + 245.
To simplify the given expression, (2x+7)(15y-5)(3x-7), we can proceed step-by-step using the distributive property:
Step 1: Multiply the first two terms, (2x+7) and (15y-5):
(2x + 7)(15y - 5) = 2x * 15y + 2x * (-5) + 7 * 15y + 7 * (-5)
Step 2: Multiply the last term, (3x-7), to the result obtained in step 1:
(2x * 15y + 2x * (-5) + 7 * 15y + 7 * (-5))(3x - 7) = (30xy - 10x + 105y - 35)(3x - 7)
Step 3: Multiply each term in the first expression by each term in the second expression:
30xy * 3x + 30xy * (-7) - 10x * 3x - 10x * (-7) + 105y * 3x + 105y * (-7) - 35 * 3x - 35 * (-7)
Step 4: Simplify each term:
90x^2y - 210xy - 30x^2 + 70x + 315xy - 735y - 105x + 245
Step 5: Combine like terms:
90x^2y - 30x^2 + 315xy - 210xy - 105x + 70x - 735y + 245
Step 6: Rearrange the terms in descending order of the variables:
90x^2y - 30x^2 + (315xy - 210xy) - (105x - 70x) - 735y + 245
Step 7: Simplify further:
90x^2y - 30x^2 + 105xy - 35x - 735y + 245
So, the simplified form of the expression (2x+7)(15y-5)(3x-7) is 90x^2y - 30x^2 + 105xy - 35x - 735y + 245.