Multiply. (5x + 7)2 A. 25×2 + 35x + 49 B. 25×2 – 70x + 49 C. 25×2 + 70x + thing D. 25×2 + 49​

Question

Multiply. (5x + 7)2

A. 25×2 + 35x + 49
B. 25×2 – 70x + 49
C. 25×2 + 70x + thing
D. 25×2 + 49​

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RI SƠ 3 years 2021-08-14T04:25:24+00:00 1 Answers 8 views 0

Answers ( )

  1. MichaelMet
    0
    2021-08-14T04:26:32+00:00
    Reply

    Answer:

    (5x + 7)² = 25x² + 70x + 49 ⇒ C

    Step-by-step explanation:

    The steps of solving the square binomial: (ax + b)²

    1. (ax + b)² = (ax + b)(ax + b)

    2. (ax + b)(ax + b) = (ax × ax) + (ax × b) + (b × ax) + (b × b) = a²x² + abx + abx + b²

    3. Add the like terms ⇒ a²x² + (abx + abx) + b² = a²x² + 2abx + b²

    Then (ax + b)² = a²x² + 2abx + b²

    Let us use the same steps to solve the question

    ∵ (5x + 7)² = (5x + 7)(5x + 7)

    ∴ (5x + 7)(5x + 7) = (5x)(5x) + (5x)(7) + (7)(5x) + (7)(7)

    ∴ (5x + 7)(5x + 7) = 25x² + 35x + 35x + 49

    → Add the like terms

    ∵ 25x² + 35x + 35x + 49 = 25x² + (35x + 35x) + 49 = 25x² + 70x + 49

    ∴ (5x + 7)(5x + 7) = 25x² + 70x + 49

    → Then equate (5x + 7)² by the right side above

    ∴ (5x + 7)² = 25x² + 70x + 49

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