QuestionExpand and simplify $(2 a+3)(4 a+5)$

Studdy Solution

STEP 1

1. We are given a binomial expression to expand and simplify.
2. The expression can be expanded using the distributive property (also known as the FOIL method for binomials).

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 $(2a + 3)(4a + 5)$ .
- First: Multiply the first terms in each binomial: $2a \times 4a = 8a^2$ . - Outer: Multiply the outer terms in the product: $2a \times 5 = 10a$ . - Inner: Multiply the inner terms in the product: $3 \times 4a = 12a$ . - Last: Multiply the last terms in each binomial: $3 \times 5 = 15$ .
Combine these results:
$8a^2 + 10a + 12a + 15$

STEP 4

Simplify the expression by combining like terms.
Combine the $a$ terms:
$10a + 12a = 22a$
The simplified expression is:
$8a^2 + 22a + 15$

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