Simplify
1) 4r+3-9r^2+7r
2) (4h^3+3h+1)-(-5h^3+6h-2)
3) 5k (3-4k)
4) (2x-3)(4x+3)
5) (4x-3)(4x+3)
My answers:
1) 11r+3-9r^2
2) this one I am confused about
3) confused
4) 7x×7
5) 8x-6
Please help me
#2:
(4h^3+3h+1)-(-5h^3+6h-2)
think of it as
(4h^3+3h+1)-1(-5h^3+6h-2)
= 4h^3 + 3h + 1 + 5h^2 - 6h + 2
= 9h^2 -3h + 3
#3
5k (3-4k)
= 15k - 20k^2 by the distributive property
#4, oh dear!!!
(2x-3)(4x+3)
= 8x^2 + 6x - 12x - 9
= 8x^2 - 6x - 9
#5 , same as #4
(4x-3)(4x+3)
= 16x^2 + 12x - 12x - 9
= 16x^2 - 9 <--- called the difference of squares
make sure you are familiar with FOIL,
F : multiply the firsts
O : multiply the "outers"
I : multiply the "inners"
L: multiply the "lasts"
Uh ye
Of course, I'll be happy to help you simplify these expressions step by step.
1) 4r + 3 - 9r^2 + 7r:
To simplify this expression, combine the like terms. The like terms are the terms that have the same variable and exponent. In this case, the like terms are 4r and 7r. So, add their coefficients (the numbers in front of the variable). The coefficient of 4r is 4 and the coefficient of 7r is 7. Their sum is 4 + 7 = 11. Therefore, we get:
11r + 3 - 9r^2.
2) (4h^3 + 3h + 1) - (-5h^3 + 6h - 2):
To simplify this expression, distribute the negative sign inside the second set of parentheses. This means changing the signs of all the terms inside those parentheses. Hence we get:
4h^3 + 3h + 1 + 5h^3 - 6h + 2.
Now, we can combine the terms with the same variable and exponent. In this case, we have 4h^3 and 5h^3. Adding their coefficients, we get 4 + 5 = 9h^3. Similarly, combining the h term, we have 3h - 6h = -3h. Lastly, the constant terms can be combined: 1 + 2 = 3. Therefore, we get:
9h^3 - 3h + 3.
3) 5k(3 - 4k):
To simplify this expression, we will apply the distributive property. Multiply the number 5k by each term inside the parentheses:
5k * 3 = 15k
5k * (-4k) = -20k^2
Therefore, the simplified expression is:
15k - 20k^2.
4) (2x - 3)(4x + 3):
To simplify this expression, we will apply the distributive property. Multiply each term from the first set of parentheses by each term from the second set of parentheses:
2x * 4x = 8x^2
2x * 3 = 6x
-3 * 4x = -12x
-3 * 3 = -9
Now, combine the like terms:
8x^2 + 6x - 12x - 9
Simplifying further:
8x^2 - 6x - 9.
5) (4x - 3)(4x + 3):
This expression is a special case known as the difference of squares, where we have the square of two terms being subtracted. In this case, it follows the pattern (a - b)(a + b). The result can be simplified using the formula:
(a - b)(a + b) = a^2 - b^2
So, applying this formula to the given expression, we have:
(4x)^2 - (3)^2 = 16x^2 - 9.
Therefore, the simplified expression is:
16x^2 - 9.
I hope this helps! Let me know if you have any further questions.