Explained: "How do you find the product (3c+4d)2?" - Plainmath

Secondary
Algebra
Algebra II
Polynomial factorization

Lauren Mullins

Answered question

2022-02-11

How do you find the product

{(3 c + 4 d)}^{2}

?

Answer & Explanation

patriette65s

Beginner2022-02-12Added 15 answers

{(3 c + 4 d)}^{2}

= (3 c + 4 d) \times (3 c + 4 d)

= 3 c \times (3 c + 4 d) + 4 d \times (3 c + 4 d)

= 3 c \times 3 c + 3 c \times 4 d + 4 d \times 3 c + 4 d \times 4 d

= 9 c^{2} + 24 c d + 16 d^{2}

Layla Humphrey

Beginner2022-02-13Added 11 answers

Explanation:
Using the special product

{(a + b)}^{2} = a^{2} + 2 a b + b^{2}

, we can set a=3c and b=4d to get

{(3 c + 4 d)}^{2} = {(3 c)}^{2} + 2 (3 c) (4 d) + {(4 d)}^{2}

= 3^{2} c^{2} + (2) (3) (4) c d + 4^{2} d^{2}

= 9 c^{2} + 24 c d + 16 d^{2}

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