To simplify the expression y^2 - 3y - 18, you can factor it:
Step 1: First, look for two numbers whose product is equal to the product of the coefficient of y^2 term (which is 1) and the constant term (which is -18) and whose sum is equal to the coefficient of the y term (which is -3).
Step 2: The two numbers are -6 and 3, because (-6) * (3) = -18 and (-6) + (3) = -3.
Step 3: Now, rewrite the expression using these numbers to factor it:
y^2 - 3y - 18 = y^2 - 6y + 3y - 18
Step 4: Group the terms and factor out the common terms:
To simplify the expression 6x^2 + 29x + 20, you can factor it:
Step 1: Look for two numbers whose product is equal to the product of the coefficient of x^2 term (which is 6) and the constant term (which is 20) and whose sum is equal to the coefficient of the x term (which is 29).
Step 2: The two numbers are 4 and 5 because (4) * (5) = 20 and (4) + (5) = 9.
Step 3: Now, rewrite the expression using these numbers to factor it:
6x^2 + 29x + 20 = 6x^2 + 4x + 5x + 20
Step 4: Group the terms and factor out the common terms:
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Answer:
To simplify the expression y^2 - 3y - 18, you can factor it:
Step 1: First, look for two numbers whose product is equal to the product of the coefficient of y^2 term (which is 1) and the constant term (which is -18) and whose sum is equal to the coefficient of the y term (which is -3).
Step 2: The two numbers are -6 and 3, because (-6) * (3) = -18 and (-6) + (3) = -3.
Step 3: Now, rewrite the expression using these numbers to factor it:
y^2 - 3y - 18 = y^2 - 6y + 3y - 18
Step 4: Group the terms and factor out the common terms:
y^2 - 6y + 3y - 18 = (y^2 - 6y) + (3y - 18) = y(y - 6) + 3(y - 6)
Step 5: Factor out the common binomial (y - 6):
y(y - 6) + 3(y - 6) = (y + 3)(y - 6)
So, the simplified expression is (y + 3)(y - 6).
To simplify the expression 6x^2 + 29x + 20, you can factor it:
Step 1: Look for two numbers whose product is equal to the product of the coefficient of x^2 term (which is 6) and the constant term (which is 20) and whose sum is equal to the coefficient of the x term (which is 29).
Step 2: The two numbers are 4 and 5 because (4) * (5) = 20 and (4) + (5) = 9.
Step 3: Now, rewrite the expression using these numbers to factor it:
6x^2 + 29x + 20 = 6x^2 + 4x + 5x + 20
Step 4: Group the terms and factor out the common terms:
6x^2 + 4x + 5x + 20 = (6x^2 + 4x) + (5x + 20) = 2x(3x + 2) + 5( x + 4)
Step 5: Factor out the common binomials:
2x(3x + 2) + 5(x + 4) = 2x(3x + 2) + 5( x + 4) = (2x + 5)(3x + 4)
So, the simplified expression is (2x + 5)(3x + 4).
Step-by-step explanation:
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