Let's solve these expressions step-by-step by factoring out the common terms and writing the simplified results:
1. Expression: [tex]\( 2x(5x + 3) + 7(5x + 3) \)[/tex]
- Factor out the common term [tex]\( (5x + 3) \)[/tex].
- The remaining terms are [tex]\( 2x \)[/tex] and [tex]\( 7 \)[/tex].
- Hence, rewrite as [tex]\( (2x + 7)(5x + 3) \)[/tex].
2. Expression: [tex]\( 8x(x + 1) + 2(x + 1) \)[/tex]
- Factor out the common term [tex]\( (x + 1) \)[/tex].
- The remaining terms are [tex]\( 8x \)[/tex] and [tex]\( 2 \)[/tex].
- Hence, rewrite as [tex]\( 2(x + 1)(4x + 1) \)[/tex].
3. Expression: [tex]\( 6x(x - 10) - 1(x - 10) \)[/tex]
- Factor out the common term [tex]\( (x - 10) \)[/tex].
- The remaining terms are [tex]\( 6x \)[/tex] and [tex]\( -1 \)[/tex].
- Hence, rewrite as [tex]\( (x - 10)(6x - 1) \)[/tex].
4. Expression: [tex]\( 1x(3x + 4) + 5(3x + 4) \)[/tex]
- Factor out the common term [tex]\( (3x + 4) \)[/tex].
- The remaining terms are [tex]\( 1x \)[/tex] and [tex]\( 5 \)[/tex].
- Hence, rewrite as [tex]\( (x + 5)(3x + 4) \)[/tex].
5. Expression: [tex]\( 3x(8x + 3) - 4(8x + 3) \)[/tex]
- Factor out the common term [tex]\( (8x + 3) \)[/tex].
- The remaining terms are [tex]\( 3x \)[/tex] and [tex]\( -4 \)[/tex].
- Hence, rewrite as [tex]\( (3x - 4)(8x + 3) \)[/tex].
6. Expression: [tex]\( 5x(2x + 6) + 2(2x + 6) \)[/tex]
- Factor out the common term [tex]\( (2x + 6) \)[/tex].
- The remaining terms are [tex]\( 5x \)[/tex] and [tex]\( 2 \)[/tex].
- Hence, rewrite as [tex]\( 2(x + 3)(5x + 2) \)[/tex].
7. Expression: [tex]\( 7x(-5x + 2) - 13(-5x + 2) \)[/tex]
- Factor out the common term [tex]\( (-5x + 2) \)[/tex].
- The remaining terms are [tex]\( 7x \)[/tex] and [tex]\( -13 \)[/tex].
- Hence, rewrite as [tex]\( -(5x - 2)(7x - 13) \)[/tex].
8. Expression (provided with a mistake): [tex]\( -4x(12x + 3) + 3(12x + \)[/tex]
- This seems incomplete and possibly contains a typographical error. Therefore, we cannot solve it without additional information.
