Here are the step-by-step solutions for the algebra problems shown in the quiz.
1. Result of $-2a(a + 3b)$
*
Step 1: Distribute $-2a$ to both terms inside the parentheses.
* $(-2a) \times (a) = -2a^2$
* $(-2a) \times (3b) = -6ab$
*
Step 2: Combine the results.
* $-2a^2 - 6ab$
*
Match: This matches option
D.
2. Subtract $4i - 3j + 2k$ from $6i - 3j - 4k$
*
Step 1: Set up the subtraction equation: $(6i - 3j - 4k) - (4i - 3j + 2k)$.
*
Step 2: Distribute the negative sign to the second group (change the signs).
* $6i - 3j - 4k - 4i + 3j - 2k$
*
Step 3: Group like terms together.
* $i$ terms: $6i - 4i = 2i$
* $j$ terms: $-3j + 3j = 0$ (they cancel out)
* $k$ terms: $-4k - 2k = -6k$
*
Step 4: Final result is $2i - 6k$.
*
Match: This matches option
C.
3. Simplify $(4c + 8d - 3e) - (6c + 2d - 2e)$
*
Step 1: Distribute the negative sign to the second bracket.
* $4c + 8d - 3e - 6c - 2d + 2e$
*
Step 2: Group like terms.
* $c$: $4c - 6c = -2c$
* $d$: $8d - 2d = 6d$
* $e$: $-3e + 2e = -e$
*
Step 3: Final result is $-2c + 6d - e$.
*
Match: This matches option
D.
4. Result of $(3c - a)(3c + a)$
*
Step 1: Recognize this as the "Difference of Squares" pattern: $(x - y)(x + y) = x^2 - y^2$.
*
Step 2: Apply the pattern. Here, $x = 3c$ and $y = a$.
* $(3c)^2 - (a)^2$
*
Step 3: Calculate the squares.
* $9c^2 - a^2$
*
Match: This matches option
C.
5. Result of $(-5x + 8y)^2$
*
Step 1: Use the perfect square formula: $(A + B)^2 = A^2 + 2AB + B^2$.
* Here, $A = -5x$ and $B = 8y$.
*
Step 2: Calculate each part.
* $A^2 = (-5x)^2 = 25x^2$
* $2AB = 2 \times (-5x) \times (8y) = -80xy$
* $B^2 = (8y)^2 = 64y^2$
*
Step 3: Combine them: $25x^2 - 80xy + 64y^2$.
*
Match: This matches option
D.
6. Simplest form of $4(2x - 5y) - 5(x + 3y)$
*
Step 1: Expand (multiply out) both brackets.
* First part: $4 \times 2x = 8x$ and $4 \times -5y = -20y$. So, $8x - 20y$.
* Second part: $-5 \times x = -5x$ and $-5 \times 3y = -15y$. So, $-5x - 15y$.
*
Step 2: Combine all terms: $8x - 20y - 5x - 15y$.
*
Step 3: Group like terms.
* $x$: $8x - 5x = 3x$
* $y$: $-20y - 15y = -35y$
*
Step 4: Final result is $3x - 35y$.
*
Match: This matches option
D.
7. Result of $(2x + 3)(3x - 5)$
*(Note: The options for question 7 are cut off in the image, but here is the correct calculation)*
*
Step 1: Use the FOIL method (First, Outer, Inner, Last).
*
First: $2x \times 3x = 6x^2$
*
Outer: $2x \times -5 = -10x$
*
Inner: $3 \times 3x = 9x$
*
Last: $3 \times -5 = -15$
*
Step 2: Combine like terms ($-10x$ and $9x$).
* $-10x + 9x = -x$
*
Step 3: Final result is $6x^2 - x - 15$.
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Final Answer:
1. D
2. C
3. D
4. C
5. D
6. D
7. $6x^2 - x - 15$
Parent Tip: Review the logic above to help your child master the concept of algebra worksheet grade 7.
