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Find the missing term.
(x+2)(x+5)
x^(2)+5x+2x+(2)*(5)
x^(2)_____+10

Find the missing term.\newline(x+2)(x+5)(x+2)(x+5)\newlinex2+5x+2x+(2)(5)x^{2}+5 x+2 x+(2) \cdot(5)\newlinex2_____+10x^{2}\_\_\_\_\_+10

Full solution

Q. Find the missing term.\newline(x+2)(x+5)(x+2)(x+5)\newlinex2+5x+2x+(2)(5)x^{2}+5 x+2 x+(2) \cdot(5)\newlinex2_____+10x^{2}\_\_\_\_\_+10
  1. Apply Distributive Property: Apply the distributive property to multiply the first term in the first binomial by both terms in the second binomial.\newline(x+2)(x+5)=x(x+5)+2(x+5)(x+2)(x+5) = x(x+5) + 2(x+5)
  2. Distribute xx: Distribute xx across the terms inside the parentheses.\\newline\)x(x+5)=x2+5xx(x+5) = x^2 + 5x
  3. Distribute 22: Distribute 22 across the terms inside the parentheses.\newline2(x+5)=2x+102(x+5) = 2x + 10
  4. Combine Terms: Combine the results from Step 22 and Step 33.\newlinex2+5x+2x+10x^2 + 5x + 2x + 10
  5. Combine Like Terms: Combine like terms 5x5x and 2x2x.\newlinex2+5x+2x+10x^2 + 5x + 2x + 10\newline=x2+(5x+2x)+10= x^2 + (5x + 2x) + 10\newline=x2+7x+10= x^2 + 7x + 10

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