Using the example: (a+b)(a+b)= a squared -b squared, we are asked to multiply and simplify (b+3d)(b-3d). Hint: Do not use distributive property.
Shouldn't the answer be b squared - 9d squared?
yes
thank you!
To multiply (b+3d)(b-3d) without using the distributive property, you can use the formula for the difference of squares.
The formula for the difference of squares is:
(a+b)(a-b) = a^2 - b^2
In this case, let's treat (b+3d) as "a" and (b-3d) as "b".
So we have:
(a+b)(a-b) = a^2 - b^2
Substituting our values:
(b+3d)(b-3d) = (b+3d)^2 - (b-3d)^2
Expanding (b+3d)^2:
(b+3d)(b+3d) = (b^2 + 6bd + 9d^2)
Expanding (b-3d)^2:
(b-3d)(b-3d) = (b^2 - 6bd + 9d^2)
Now, substituting the two expansions back into our original expression:
(b+3d)(b-3d) = (b^2 + 6bd + 9d^2) - (b^2 - 6bd + 9d^2)
Simplifying the expression:
(b+3d)(b-3d) = b^2 + 6bd + 9d^2 - b^2 + 6bd - 9d^2
Combining like terms:
(b+3d)(b-3d) = (b^2 - b^2) + (6bd + 6bd) + (9d^2 - 9d^2)
Simplifying further:
(b+3d)(b-3d) = 0 + 12bd + 0
Therefore, the answer is 12bd.
So the expression (b+3d)(b-3d) simplifies to 12bd, not b^2 - 9d^2.