Math  /  Algebra

Question(3a21)(3a2+5)\left(3 a^{2}-1\right)\left(-3 a^{2}+5\right)

Studdy Solution

STEP 1

1. We are asked to simplify the expression.
2. The expression involves the multiplication of two binomials.
3. We will use the distributive property (also known as the FOIL method for binomials) to expand the expression.

STEP 2

1. Apply the distributive property to expand the expression.
2. Simplify the resulting expression by combining like terms.

STEP 3

Apply the distributive property (FOIL method) to expand the expression:
(3a21)(3a2+5)=(3a2)(3a2)+(3a2)(5)+(1)(3a2)+(1)(5)(3a^2 - 1)(-3a^2 + 5) = (3a^2)(-3a^2) + (3a^2)(5) + (-1)(-3a^2) + (-1)(5)

STEP 4

Calculate each term from the expansion:
1. (3a2)(3a2)=9a4(3a^2)(-3a^2) = -9a^4
2. (3a2)(5)=15a2(3a^2)(5) = 15a^2
3. (1)(3a2)=3a2(-1)(-3a^2) = 3a^2
4. (1)(5)=5(-1)(5) = -5

STEP 5

Combine the like terms from the expanded expression:
9a4+15a2+3a25-9a^4 + 15a^2 + 3a^2 - 5
Combine the a2a^2 terms:
9a4+(15a2+3a2)5=9a4+18a25-9a^4 + (15a^2 + 3a^2) - 5 = -9a^4 + 18a^2 - 5
The simplified expression is:
9a4+18a25\boxed{-9a^4 + 18a^2 - 5}

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