Expand and simplify the following expressions:

1. \((X+6)(x+9)\)

2. \((X-5)(x+2)\)

3. \((X-1)(x-7)\)

4. \((4x+9)(3x+8)\)

5. \((3x-8)(2x-1)\)

6. \((X+9)^2\)

7. \((3x+2)^2\)

( x + 6 ) ( x + 9 ) = x 2 + 9 x + 6 x + 54 = x 2 + 15 x + 54 ( x − 5 ) ( x + 2 ) = x 2 + 2 x − 5 x − 10 = x 2 − 3 x − 10 ( x − 1 ) ( x − 7 ) = x 2 − 7 x − x + 7 = x 2 − 6 x + 7 ( 4 x + 9 ) ( 3 x + 8 ) = 12 x 2 + 32 x + 27 x + 72 = 12 x 2 + 59 x + 72 ( 3 x − 8 ) ( 2 x − 1 ) = 6 x 2 − 3 x − 16 x + 8 = 6 x 2 − 19 x + 8 ( x + 9 ) 2 = x 2 + 2 ⋅ x ⋅ 9 + 9 2 = x 2 + 18 x + 81 ( 3 x + 2 ) 2 = ( 3 x ) 2 + 2 ⋅ 3 x ⋅ 2 + 2 2 = 9 x 2 + 12 x + 4

Answered by kate200468 | 2024-06-10

The answer involves expanding and simplifying seven algebraic expressions using the distributive property. Each expression is solved step-by-step, combining like terms where necessary. This process applies basic algebraic principles to achieve the final simplified results.
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Answered by kate200468 | 2024-10-26