Question

(2x+ y + 5)(2x + y + 7) ​

Answer 1

Step-by-step explanation:

$(2x + y + 5)(2x + y + 7)$

Multiplying each term of (2x+y+5) with (2x+y+7)

$= 2x \times 2x + 2x \times y + 2x \times 7 + 2x \times y + y \times y + y \times 7 + 5 \times 2x + 5 \times y + 5 \times 7$

$= 4 {x}^{2} + 2xy + 14x + 2xy + {y}^{2} + 7y + 10x + 5y + 35$

$= 4 {x}^{2} + {y}^{2} + 4xy + 24x + 12y + 35$

Answer 2

Answer:

$\large{ \bold{4 {x}^{2} + {y}^{2} + 8xy + 24x + 12y + 35}}$

Step-by-step explanation:

$(a +b)(a - b) = {a}^{2} - {b}^{2} \\ \\ {(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) \\ \\ given \\ \\ (2x + y + 5)(2x + y + 7) \\ \\ = ((2x + y + 6) - 1)((2x + y + 6) + 1) \\ \\ = {(2x + y + 6)}^{2} - {1}^{2} \\ \\ = (4 {x}^{2} + {y}^{2} + 36 + 2(4xy + 6y + 12x)) - 1 \\ \\ = 4 {x}^{2} + {y}^{2} + 8xy + 24x + 12y + 35$

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