1.(n-2)(3n+7)+2n(2n+3)

factor each expression fully:

2. 4xsquared-25

1.(n-2)(3n+7)+2n(2n+3)

We’ll start with (n-2)(3n+7)

Use the FOIL method to simplify: First, Outside, Inside, Last.

Multiply the first numbers of each bracket (n and 3n), the outside numbers (n and 7), the inside numbers (-2 and 3n) and the last numbers (-2 and 7)

F= 3n×n= 3n²

O= n×7= 7n

I= -2×3n= -6n

L= -2×7= -14

Add them together, you get 3n² + n -14.

The second part is 2n(2n+3)

Multiply both numbers inside the bracket by 2n

2n×2n= 4n²

3×2n= 6n

Add these terms with the previous ones

7n² + 7n -14

Because they all have a common factor of 7, we can represent the equation as

7(n² + n -2)

2. 4x²-25

To factor this, we convert it into two expressions that we multiply together (like converting -9 into 3×-3)

2x × 2x= 4x²

5 × -5= -25

The answer is (2x+5)(2x-5)

\( 1.\\(n-2)(3n+7)+2n(2n+3)\\\\=n\cdot3n+n\cdot7-2\cdot3n-2\cdot7+2n\cdot2n+2n\cdot3\\\\=3n^2+7n-6n-14+4n^2+6n\\\\=7n^2+7n-14 \)

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\( 2.\\4x^2-25=(2x)^2-5^2=(2x-5)(2x+5) \)